the space division multiple access protocol: asynchronous implementation and performance

computer communicatii

ELSEVIER Computer Communications 2 I (1998) 227-242

The Space Division Multiple Access Protocol: asynchronous implementation and performance

Lewis Barnett

Department of Mathematics and Cornpurer Science, University of Richmond, Richmond, VA 23173. USA

Received 26 September 1997; accepted 26 September 1997

Abstract

Implementation of communication protocols based on collision resolution algorithms on broadcast bus networks requires a level of synchronization among participating stations such that idle steps in the algorithm can be globally and unambiguously detected. We present performance results for two collision resolution algorithms, the Capetanakis tree protocol and space division multiple access, a new

algorithm, using a previously described asynchronous implementation technique. Two variants of space division multiple access are discussed. One variant improves upon the mechanism for implementing the necessary synchronization. The other relaxes the requirements for a station with a new packet joining the resolution algorithm. The performance effects of these variations are examined by simulating the behavior of the protocols. The variants are shown to improve the performance of the protocol under some traffic loads. In addition, one of the

variants is shown to improve on the fairness of the original algorithm over a variety of offered loads and maximum data rates. 0 1998 Elsevier Science B.V.

Keywords: Local area network; MAC protocol; Collision resolution algorithm

1. Introduction

Collision resolution algorithms (CRAs) are an alternative

method for broadcast bus medium access control (MAC) which have several desirable properties. These algorithms

use feedback from the channel to resolve collisions, reduc-

ing the average delay and variance of delay experienced by other access mechanisms. Offsetting these desirable proper-

ties is the requirement that all stations need complete information on channel history. These algorithms have usually

been discussed in terms of slotted transmission channels and fixed-length packet transmission.

Protocols based on CRAs operate by initially allowing all stations on the network with a packet ready for transmission to transmit in a slot. If a collision occurs, the stations are

divided into two groups according to some globally agreed upon criterion. The stations in the “first” group are allowed

to transmit in the next slot, and if a collision results, the

group is further subdivided and the resolution proceeds recursively. When the first group has been resolved, the second group is allowed to resolve. The time required to successfully transmit all of the packets involved in the original collision is referred to as a collision resolution epoch. Stations which become ready after the beginning of an epoch must wait for the epoch to end before attempting

0140-3664/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved PII SO140-3664(97)00184-9

transmission. Several different algorithms have been pro- posed in the literature based on different criteria for per-

forming the subdivision. The Capetanakis tree protocols used a uniquely assigned or randomly generated address

for each station [ 1,2]. First-come first-served protocol uses

the arrival time of packets within an enabled transmission

“window” as the subdivision criterion [3,4]. More recently, interest in packetized voice and other time-constrained applications has led to the proposal of variants of the first-

come first-served protocol which take transmission dead- lines into account [5].

Practical application of these techniques is limited by the necessity of synchronous operation of the stations partici-

pating in the protocol. The required level of synchronization is difficult to achieve in a bus structured local area network (LAN) using the carrier sense multiple access with collision

detection (CSMAKD) technique [6]. For example, consider the situation where the operation of a CRA results in an

algorithm step where no stations have permission to trans-

mit. As a result, no activity indicating the outcome of the algorithm step appears on the network. How do stations decide when this “idle step” is officially over so that they can proceed with the algorithm? This question has been investigated by Towsley [7] and Molle [8]. In both cases, asynchronous operation used knowledge of the maximum

228 L. BarnetKomputer Communications 21 (1998) 227-242

propagation delay on the network to determine the end of

“steps” in the algorithm. This technique can be problematic when counting successive idle steps if there is a significant

difference in the clock rates of the participating stations. To

avoid this potential problem, Molloy presented a mechanism for signaling the end of idle steps in a collision resolu-

tion algorithm by causing an intentional collision which is

consistently observable by all stations on the network [9].

Variable length messages were considered by Wu and

Chang [lo]. Their work describes a protocol where mes-

sages are divided into fixed length packets, with the first-

come first-served algorithm being used to arbitrate control of the bus for transmission of trains of such packets.

There has been a recent increase in interest in commu-

nication protocols based on CRAs. Control applications for

vehicles is one potential application area. There has also

been interest in CRA-based LAN network protocols tailored for distributed real time applications [ 111. CRAs also seem

promising in the area of time-constrained applications, such

as packetized voice [5].

In this paper, we first describe a new CRA, the space

division multiple access protocol (SDMA). This protocol

uses Molloy’s method for signaling the end of idle steps and takes advantage of information about the position of

stations on the network in its operation. We then describe two variant implementation strategies for CRAs on broadcast bus networks. Through simulation, the performance of

these algorithms is shown to be competitive with Ethernet in terms of overall network utilization and much better than

Ethernet in terms of the variability of delay experienced by

transmitting stations for the traditional 10 Mbps CSMAKD bus. In addition, the protocols are shown to provide fairer

access to the channel than Ethernet under a variety of traffic

loads. Finally, the behavior of the protocol as data rates

increase from 10 Mbps to 100 Mbps is examined. The remainder of the paper is organized as follows. First,

some of the difficulties of implementing CRAs in a broad-

cast bus network are discussed. Next, the operation of the SDMA protocol and its variants is described. Presentation of simulation results on the performance of SDMA and its

variants under various traffic loads and network configura- tions follows. Finally, a summary and some conclusions are

presented.

2. Asynchronous implementation of collision resolution

Consider the problem of establishing the level of synchronization required by CRAs on a typical CSMA/CD bus. Such a bus has no inherent slotting and no shared control signaling. A method for implementing collision resolution algorithms on such an asynchronous (unslotted) broadcast bus was presented by Molloy [9]. The problem with implementing most CRAs on an asynchronous bus is that it is difficult for stations to agree on exactly when an algorithm step ends if it produces no activity on the network. Since

there are no slot boundaries on an asynchronous bus, some other mechanism must be employed to signal the end of

such an idle step in the protocol. The method presented by

Molloy requires that when a period equal in duration to twice the maximum propagation delay of the network during which no transmissions occur is observed, some subset

of the stations on the network should transmit. This subset must consist of at least two stations. This transmission is

intended to produce a collision which signals to all stations

on the network that an idle step has occurred and is now

over. We refer to a collision of this type as an idle marking

collision. This collision is visible to all stations on the net-

work and acts as a signal to proceed with the next step of the

algorithm. The most easily identified subset to participate in

the idle marking collision is the set of all stations on the

network. Choosing an alternative subset for this purpose is discussed in Section 3.2.

This mechanism allows CRAs to be implemented on unslotted broadcast bus networks without the addition of

special hardware such as globally accessible clocks or separate control lines. There is therefore no restriction

(other than those imposed by the CSMAKD mechanism

itself) on the lengths of packets. Slotted media also impose additional latency for the initial transmission attempt, since

a station must wait for the next slot boundary before attempting transmission. This additional latency is elimi- nated in protocols using Molloy’s method, improving the

low load performance of these algorithms.

3. The space division multiple access protocol

The SDMA protocol is a specialization of the class of

protocols which use a unique address to perform collision

resolution, such as the Capetanakis tree protocol. The basic operation of such protocols was described in Section 1.

Protocols based on CRAs typically do not require any correlation between the address of a station and the location of

the station on the network. This simplifies adding new stations to a network; it is only necessary to find a unique

address to assign to the new station. However, performance improvements can result from using information about the actual positions of stations on the network in the collision

resolution process. The SDMA protocol exploits one such

improvement. (Various unidirectional broadcast protocols

such as Expressnet [ 121, DQDB [ 131 and Hymap [ 141

have made use of upstream/downstream positional information. These protocols are intended for use on folded bus or dual bus layouts.)

We shall describe the original SDMA protocol and two variants which address limitations in the original and in the asynchronous implementation technique.

3.1. The original protocol

The SDMA protocol is similar to the address-based

L. BamerKomputer Communications 21 (1998) 227-242 229

Capetanakis protocol with one important difference: the

address space for stations corresponds directly to the physical

length of the network. If the address of the station is inter-

preted as a location (e.g., distance from one end of the cable),

then the collision clear time can be reduced with each address space subdivision. The collision clear time is the amount of

time between the detection of a collision by a station and the

time at which the station is guaranteed that all signals gener-

ated by stations involved in the collision have been received.

To see why this time can be reduced under the conditions described above, consider the situation when a collision

occurs in such a network. Let L be the length of the network. When a collision occurs, the protocol divides the stations into

two subsets, one subset containing addresses less than W2

and the other subset containing stations whose address is

greater than or equal to L/2. The protocol first enables the

stations with addresses less than L/2 to transmit at the next

opportunity. Since addresses correspond to locations, this corresponds to a physical partitioning of the cable, with all

the stations in the enabled subset on the same half of the

network. This means that the maximum propagation delay

between enabled stations will be at most half of the full propagation delay of the network. So, should another collision occur, the collision itself will be of shorter duration

owing to the proximity of the colliding stations (each detects

the signal of the other and aborts transmission sooner), and the subsequent channel clear time will be half what it was for

the previous step. On sparsely populated cables, further gains can be made by keeping track of the unused station positions.

If an enabled range of addresses consists wholly of unused positions, a step can be skipped.

There are several restrictions imposed by the SDMA

scheme. First, the protocol is biased in favor of stations with low addresses. For example, consider a situation in

which a high-address station generates a new packet just after the beginning of a collision resolution epoch. Since

the station cannot join the current resolution round, it is possible for any station with a lower address to transmit a

packet in the current round and the next round before the station with the higher address is allowed to transmit one packet. Note that this scenario can occur in any CRA which

uses addresses as the criterion for subdivision. It is simply rendered more apparent by the correlation of addresses with

station locations in SDMA. Second, stations are required to

continuously monitor the channel at all times as in the first- come, first-served protocol. This makes it more difficult for new stations to be added to a network. Third, SDMA

expects the network to be a single linear cable, a significant layout limitation. To mitigate this situation, the protocol can

be adapted to handle branching layouts by mapping addresses to create a logical linear cable with length equal to the sum of the lengths of the branches. This mapping must, of course, assign addresses such that stations on different branches are not assigned the same address. While this addresses typical layouts incorporating repeaters, there is no direct analog to SDMA on the increasingly popular

1OBaseT star layout. The notion of position would have to

be replaced by the distance of stations from the hub, and

although some performance gain could result from using

this distance as the subdivision metric, the improvement

would not be as great as in the bus layout. The restriction to a traditional bus layout means that SDMA suffers from

the same limitations as do CSMA/CD protocols in terms of

the distance/bandwidth product. As bandwidth increases,

the maximum distance of an SDMA network would have

to decrease to maintain a constant minimum packet size. These limitations restrict the range of applications for

which SDMA is appropriate. There are obvious difficulties

involved in relocating stations on a network, so the best use

of SDMA would be in applications where the locations of

stations are fixed. Such applications might involve networks

of computing elements, device controllers or intelligent sen- sors embedded in structures or vehicles.

3.2. SDMA variants

We now describe two variants of the SDMA protocol

which result in improvements in the overall performance

of the protocol. The first, SDMA with restricted topology (SDMA-RT), requires that the stations on the network be

evenly spaced with no gaps. This allows the size of the set of stations participating in an idle marking collision to be

reduced under some circumstances, resulting in better over-

all throughput. The second, SDMA with relaxed entry

(SDMA-RE), gains some performance improvement by allowing stations to join collision resolution epochs while

they are in progress, rather than forcing newly ready stations to wait for the end of the current epoch before joining the

algorithm. In the discussion that follows, we make use of

several new terms.

Definition 1: A ready station is a station which is cur-

rently attempting to transmit a packet.

Definition 2: The currently enabled segment of the network is the portion of the network from which trans-

missions are allowed during the current step of the algorithm.

Definition 3: An enabled station is a station whose

address falls within the currently enabled segment. Definition 4: A regularly spaced network is a network

in which stations are placed at regular intervals with no gaps in the pattern.

3.2.1. SDMA with restricted topology

The original SDMA protocol uses the idle marking

collision technique with all stations on the network participating in each idle marking collision. While it is possible to identify smaller subsets of stations to fulfil this role at each idle step, the subset must be chosen carefully. It is not sufficient to require that stations in the currently enabled segment of the network transmit, because this may result in an empty subset. To see how this could occur, consider

230 L. Burnett/Computer Communications 21 (1998) 227-242

Sl s2

s 1.1 s 1.2 II s 2.1 s 2.2

nnnn 1 2 3 4 5 6

Fig. I. A collision resulting in an “empty” enabled network segment.

Fig. 1. The horizontal line is the cable, with the numbered

tick marks representing stations. The shaded chevrons

depict the propagation of signals originating from some of the stations in space (the horizontal axis) and time (the

vertical axis, advancing downwards). Recall that the original SDMA protocol puts no restrictions on where a station

can be placed on the network. When the original collision

involving stations 1, 2, 3 and 4 occurs, the algorithm sub-

divides the network into two segments, labeled S, and SZ, with the stations in Sr enabled in the next step of the algorithm. These stations transmit and collide again, resulting

in a further subdivision of St into S,,, and S1,2. Stations 1 and 2 collide a third time, and are eventually resolved.

When the resolution of the stations in S,.r is completed, S1,2 is enabled. Since there are no stations in this segment of the network, no transmissions are attempted, resulting in an idle step in the algorithm. However, if only stations in the

currently enabled network segment were required to participate in the idle marking collision, no such collision would

be generated in this situation, and the protocol would fail, absent some fallback mechanism for dealing with such a situation.

It is possible to identify several candidate subsets to participate in the idle marking collision. We would like to keep the set as small and close together as possible to limit the duration of the idle marking collision. It would also be desirable to limit membership in the set to stations which are actively attempting to transmit. This set of stations may also be empty. This situation would occur if stations 3 and 4

in Fig. I were not currently trying to transmit. We have already demonstrated that in the case of an unrestricted

layout, the currently enabled segment may be empty.

Given the nature of the SDMA algorithm, the smallest set

of stations that is guaranteed to be nonempty is the set of

stations from the “parent” segment of the current segment (segment S, in the example of Fig. 1).

If we assume that the network is regularly spaced, then

we are able to use the smallest possible subset of stations for the idle marking collision, those in the currently enabled

segment of the network. Regular spacing implies that

every possible subinterval contains at least one station. If

we make no restriction on the number of stations, it is pos-

sible for the algorithm to enter a state in which the enabled interval consists of a single station which is not ready. In

such a state, the transmission by this station to mark the end

of the idle would not collide with any other transmission, producing a successful packet. Since the operation of the protocol in all cases is the same for either a recognized idle

step or a successful transmission, this situation is not of great concern. However, to avoid any potential confusion

about the destination of such a packet, we shall assume that

it is addressed to a nonexistent station. We refer to the variant of SDMA which uses this subset as SDMA with

restricted topology, or SDMA-RT.

3.2.2. SDMA with relaxed entry

Most CRAs require stations which become ready (i.e.,

have a new packet to send) while a collision resolution

epoch is in progress to wait until the current epoch com- pletes to make their first transmission attempt. The nature of

the unfairness in the SDMA protocol noted in Section 4.2 is in part attributable to this strategy: stations with lower

addresses resolve sooner and, thus, are more likely to become ready again before the beginning of the next

epoch. We investigated the effects of removing this restriction on joining in-progress resolution epochs. For SDMA,

allowing stations to join an epoch in progress does not cause any inconsistency in the algorithm. Since ready stations in

the successfully resolved portion of the network will not be

re-enabled before the end of the current epoch, new ready stations in this part of the network will see no difference between this arrangement and the original protocol; they

will wait until the next resolution epoch to transmit. How- ever, stations in the unresolved portion of the network will

participate in the current resolution and transmit much sooner than they would have under the original protocol. This arrangement would seem to favor the stations which were penalized under the original protocol, since the resolved segment of the network grows from low addresses to high addresses. Because segments that have completed resolution are never re-enabled during the same epoch, the protocol still guarantees that no station is allowed to transmit more than once in a given epoch. We refer to this variant of the protocol as SDMA with relaxed entry or SDMA-RE.

L. BaneftKomputer Communications 21 (1998) 227-242 231

3.3. Simulation

Three SDMA variants, Ethernet and the Capetanakis tree

protocol are compared in this paper. The Capetanakis protocol was chosen because it is the CRA which SDMA most closely resembles. The protocols were simulated by using a

custom simulation package called Netsim, written by the author. Netsim uses the discrete event simulation method

to simulate a finite network of stations. Modeling of colli-

sions is very detailed, taking into account the positions of all stations involved in the collision and the effects of propaga-

tion delay on the detection time of the beginning and end of

collisions at all stations on the network. This point is parti- cularly important in accurately modeling SDMA, which

depends on reducing the length of collision bursts for

the performance improvement it achieves over similar

algorithms. Netsim also provides very flexible specification of packet length and inter-arrival time distributions, allowing realistic traffic loads to be simulated. Netsim is

described in more detail in [ 151.

The simulation parameters specified 32 regularly spaced

stations producing identical traffic loads. We consider three packet length distributions: fixed-length maximum-sized

packets (1526 bytes, which includes the packet preamble),

small fixed-length packets (76 bytes), and a discrete packet distribution abstracted from observations of the University of Richmond campus Ethernet which had a mean packet

length of 252 bytes. We present results in two categories: performance comparison of the protocols for 10 Mbps contention bus networks, and comparison of the protocols with

capacity loads as the effective data rate of the network increases.

The discrete distribution is shown in Table 1. The measured network was a single segment of a larger campus

network, which connected 20 workstations from various vendors. One of the connected machines was a file server

(primarily used for faculty accounts) and another was a mail, Domain Name, and print server. The segment is con-

nected to the building network with a DEC Bridge 90, and

individual computers are connected via twisted pair to DEC Repeater 9OTs. Samples of 10 000 packets were made at 1 h intervals over a period of 24 h on a typical work day. The

Table I Discrete packet-length distribution

Bytes Percentage of packets

75 47.5

105 4.4

135 18.0

165 16.3

444 2.6

889 0.8

1065 3.4

1305 0.4

1515 6.6

average packet size observed is much smaller than that

reported in other studies. For example, Gusella reported

an average packet size of 578 bytes [16]. We attribute the

difference primarily to three factors. First, none of the com-

puters on the measured segment were diskless, so interac- tion with the file server generally did not involve paging.

Second, it was discovered that the DEC networking equip-

ment contributed a significant number of small packets used

for management purposes to the traffic on the network.

These packets made up approximately 23% of the total

packets observed. The three packet-length distributions considered in

this work represent the best case for overall efficiency

(maximum-sized packets), the worst case (small packets)

and a realistic intermediate packet-length distribution. All

experiments used an exponential distribution of packet

inter-arrival times. The simulation concentrates on the behavior of the medium access mechanism, so no buffering in the stations is modeled.

The Capetanakis tree protocol results are for an asynchro-

nous version of the protocol constructed by using the idle

marking collision technique described in Section 2. The

simulation is essentially the same as the SDMA simulation,

except that the collision duration is not halved with each subdivision of the interval of enabled addresses. This simu-

lates the version of the Capetanakis protocol which uses unique addresses rather than coin flips to generate address

bits. Though the Capetanakis protocol does not correlate

addresses with station locations, this was not modeled in the Capetanakis simulation used here. Both the SDMA and Capetanakis implementations incorporate the Massey

improvement, where colliding stations that see an idle step in the left subinterval immediately subdivide rather than

transmitting in the right subinterval and colliding again [ 171.

The quantities reported were produced by averaging the results of three runs for each set of parameters. At least

100 000 packets were transmitted in each run.

4. Performance of SDMA

It was expected that the Ethernet protocol would prove superior to the SDMA protocol under light traffic condi-

tions, the situation for which the Ethernet protocol was designed. It was further expected that the collision resolu-

tion strategy employed by the SDMA protocol would result

in higher overall throughput and lower overall delay under conditions where the network was more heavily loaded. It was also expected that SDMA’s performance would be

slightly better than an asynchronous implementation of the Capetanakis tree protocol, the CRA to which it is most similar, in both overall throughput and average delay.

SDMA-RT improves on the overall utilization of the original protocol by decreasing the overhead for idle marking collisions. It exhibits little or no difference from SDMA in terms of fairness of access. On the other hand, SDMA-RE

232 L. BamettlComputer Communications 21 (1998) 227-242

c .s

0.6

Q ,N

5 0.4

1.5 Offered load

Fig. 2. Average utilization versus offered load for the packet mixture with exponentially distributed arrivals.

was expected to mitigate the location bias of SDMA by

allowing stations to eliminate the wait for the end of the current collision resolution epoch before joining the

algorithm. Simulation shows that this is in fact the case over an important range of offered loads.

We discuss the performance of the protocols in terms of

average utilization, average delay, variance of delay, and fairness (represented as the standard deviation of individual station throughput) in the following sections.

4.1. Pe$ormance on 10 Mbps networks

For comparisons of SDMA with the Capetanakis protocol

and Ethernet, we present only results for the packet mixture here. The advantages displayed by SDMA were also present to a lesser extent in the maximum-sized packet load and to a

greater extent in the small packet load. The complete performance comparison for 10 Mbps networks is given in

[18]. In the comparison of the three SDMA variants, we show results for all three traffic patterns.

4.1.1. Average network utilization

Fig. 2 shows the average network utilization as a percen-

tage of the total capacity of the network versus the offered

traffic load, also presented as a percentage of the capacity of the network. Offered load is the sum of the loads presented by each station running on an otherwise idle network and is

a measure of the traffic that the stations are attempting to introduce onto the network. The figure shows that, contrary to expectations, under light loads (Offered load < I), SDMA does achieve higher utilization of the network.

This situation becomes more pronounced when the offered

load approaches and exceeds the capacity of the network. At an offered load level of 200% of capacity, SDMA achieves a

utilization of 82.4%, as compared with 81.4% for Capeta- nakis and 71.7% for Ethernet. The difference between

SDMA and Capetanakis is significant at the 95% confidence level over the range of offered loads from approximately

80% to the highest load considered. Figs. 3-5 show the average overall utilization of the net-

work for the three SDMA variants versus the offered load

1.0

0.6

r .$

0.6

a = 5 0.4

1.5 Offered load

Fig. 3. Average utilization for SDMA variants with traffic consisting of 1526 byte packets.

L. BarnettKomputer Communications 21 (1998) 227-242 233

0.8

c .g

0.6

Q 4

5 0.4

1.5

Offered load

Fig. 4. Average utilization for SDMA variants with traffic consisting of the packet mixture.

for the three traffic loads discussed in Section 3.3. In all

three cases, there is little to distinguish between the three protocols a low loads, since all follow the CSMA/CD dis-

cipline for initial access to the medium. For maximum-sized

packets there is little difference in overall utilization over

the entire range of loads considered. For this load, the transmission time of the large packets dominates other factors in

determining the utilization of these three protocol variants. Results for the packet mixture and the small packet loads

show a larger distinction among the three protocols. When the load is less than the capacity of the network, both of the

variants show an advantage over the original SDMA in maximum utilization, with SDMA-RE demonstrating a

slight advantage over SDMA-RT. As the load increases, SDMA-RE maintains its advantage, while the utilization

of SDMA-RT approaches the level of SDMA. This reflects the fact that, as the network becomes busier and the number

of stations involved in each collision increases, the number of idle steps in the operation of the algorithm (from which

SDMA-RT gains its advantage) decreases. For the packet

mixture at the highest offered load considered (approximately 300% of capacity), the average utilization for

SDMA was 83.1%, versus 83.5% for SDMA-RT and

84.1% for SDMA-RE. As was the case in the comparison

with the Capetanakis protocol in Section 4, the difference

between the protocols is significant at the 95% confidence level for the range of offered loads between 80% and the

maximum load considered. At a similar load for the small

packet traffic pattern, the utilization for SDMA was 60.8%, versus 61.2% for SDMA-RT and 63.5% for SDMA-RE.

4.1.2. Average delay

Fig. 6 shows the average queueing delay for packets in

seconds versus average utilization. The average packet from the packet mixture takes approximately 200 ms to transmit.

This number is reflected in the low load values shown in this figure. The average delay for Ethernet is only slightly higher

than the transmission time at low offered load levels. This

behavior is matched by both of the CRAs, since they also transmit packets immediately when there is no contention.

0.80

0.60

1.5

Offered load

Fig. 5. Average utilization for SDMA variants with traffic consisting of 76 byte packets

234 L. BarnettKomputer Communications 21 (1998) 227-242

z .ti $ 0.004 -

x

0.0 0.2 0.4 0.6 0.6 1.0

Fig. 6. Average delay versus utilization for the packet mixture with expo- Fig. 8. Average delay for SDMA variants with traffic consisting of the

nential arrivals. packet mixture.

As the load increases and contention for the channel begins,

the two CRAs demonstrate a clear advantage over Ethernet, with SDMA experiencing slightly lower average delay than

the Capetanakis protocol. At an offered load of approxi-

mately 75%, Ethernet’s average delay is 2.13 ms, the Capetanakis protocol’s delay is 1.34 ms, and SDMA’s

delay is 1.24 ms. As the load increases to approximately the capacity of the network, the Ethernet delay is 3.71 ms versus 2.53 ms for Capetanakis and 2.37 ms for SDMA.

The difference between average delay for SDMA and Capetanakis is significant at the 95% confidence level

over the range of offered loads from approximately 50%

through the highest loads considered.

The picture of the relative performance of the three SDMA variants indicated in Section 4.1.1 is mirrored as expected by the average delay behavior of the three proto-

cols, shown in Figs. 7-9. It is worth noting that although the curves appear to be asymptotic over the loads shown in

0.040

0.030

3 3 * 0.020

Jl

$

0.010

0.000 (

! .,,,.--il

0.2 0.4 0.6 0.6 1.0 Utilization

Fig. 7. Average delay for SDMA variants with traffic consisting of Fig. 9. Average delay for SDMA variants with traffic consisting of 76 byte

1526 byte packets. packets.

0.0060

0.0000 0.0 0.2 0.4 0.6 0.6 1.0

Utilization

these figures, plotting the delay against the offered load shows a steep increase over the region between 50% offered

load and 200% offered load, after which the rate of increase

moderates significantly.

4.1.3. Variance of delay

Fig. 10 shows the variance of the packet delay versus the

network utilization for the three protocols. Lower variance of delay is a well-known advantage of CRAs over random backoff collision handling methods, as demonstrated by

these figures. At low loads where little contention occurs, there is little difference between the three protocols. As

contention begins, the variance of delay for Ethernet

increases much more rapidly than for either of the CRAs. Once the traffic becomes heavy the SDMA algorithm

resolves collisions among larger numbers of stations more efficiently than Ethernet. When packets are involved in such

collisions, the delay they experience is much more regular

than Ethernet packets transmitted under similar load

0.0030

0.0020

H 3 2 x

0.0010

0.0000 0.0 0.2 0.4 0.6 0.6

Utilization

L. BameftKomputer Communications 21 (1998) 227-242 235

0” 5.0e-06

o.Oe+Oo 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Utilization Utilization

Fig. 10. Delay variance versus utilization for the packet mixture with expo- Fig. 12. Delay variance for SDMA variants with traffic consisting of the

nential arrivals. packet mixture.

conditions owing to the unpredictability of Ethernet’s bin-

ary exponential backoff algorithm. Though not evident from

this figure, the variance of delay for the two CRAs levels off and remains steady as offered load increases past the

capacity of the network.

Figs. 1 1 - 13 show the variance of the delay for the SDMA variants versus offered load for the three traffic patterns. As for the previous metrics, little can be said about the relative behavior of the three variants under the load composed of

large packets. However, it is clear under the other two loads that the variance for SDMA-RE is much worse than the

variance for the other two variants. Fig. 12 also suggests

that SDMA-RT has slightly better variance of delay than SDMA over part of the offered load range.

4.2. Location bias of SDMA

The primary feature of the SDMA protocol is that it takes advantage of the actual positions of stations on the network

0.00025

0.00020

$ 5 0.00015 ‘Z F

E $ 0.00010

0.00005

o.ooooo 0.0 0.2 0.4 0.6 0.8 1.0

Utilization Utilization

Fig. Il. Delay variance for SDMA variants with traffic consisting of Fig. 13. Delay variance for SDMA variants with traffic consisting of

1526 byte packets. 76 byte packets.

8 5 .- 5 1 e-05

s 0”

B-06

to achieve an advantage in overall network performance over similar protocols which do not take advantage of

such information. It is therefore not surprising that stations

at different locations on the network experience different

levels of responsiveness. Similar effects have been observed

in other protocols for different types of network that make use of the location of stations as part of their protocol [ 191. Simulation results indicate that the SDMA protocol gives a

significant performance advantage to those stations which are considered to have low addresses on the network, i.e.,

those which are closest to the “left hand” end of the cable - addresses are calculated by distance from this end of the

cable. Fig. 14 shows the average utilization and delay for each station for SDMA and Ethernet. (The Capetanakis tree

protocol is not included in this comparison because the simulation of the protocol did not decouple the station

addresses from the physical location of the station. The

Capetanakis protocol should have better behavior in terms

2e-05

1.5e-05

1 e-05

58-06

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6

236 L. BarnettKhnputer Communications 2/(1998) 227-242

(a) ( W

0.008

SDMA mlxed lengths SDMA. mixed lengths

0.00 0.000 0 4 8 12 16 20 24 28 32 0 4 8 12 16 20 24 28 32

Station number

0.00 0 4 0 12 16 20 24 28 32

Station number

Station number

Ethernet, mtxed [email protected]

0.000 0 4 8 12 16 20 24 28 32

Station number

Fig. 14. Station utilization and delay for the packet mixture. 0 is offered load.

of fairness than SDMA.) Results are shown for offered loads of approximately 50%, 100% and 200% of capacity. The bias is demonstrated most strongly under heavy overloads,

and is not evident under the more normal 50% load. As Fig. 14(c) and Fig. 14(d) show, Ethernet also displays a location

bias under the same circumstances, although it is stations at

either end of the network which suffer. This effect was noted by Gonsalves and Tobagi [20].

To provide a direct comparison of the unfairness of the two protocols, Fig. 15 shows the standard deviation of utilization at individual stations versus offered load. The spread is much smaller for SDMA than for Ethernet for any load greater than 50%. At offered load approximately equal to the capacity of the network, the standard deviation for SDMA is 0.0013, versus 0.0021 for Ethernet.

Figs. 16-18 show the standard deviation of per station

utilization versus the offered load for the three SDMA variants. Recall that the motivation for the design of SDMA-RE was the location bias of the original SDMA protocol. These

figures show that the strategy adopted by SDMA-RE is only

partially successful. Over the range of loads from roughly

the point at which contention begins (which varies for the three loads) up to loads of approximately 200% of capacity, the spread of utilization among the hosts on the network is lower for SDMA-RE than for the other two variants. For any load in excess of 200% of capacity, SDMA-RE exhibits unfairness which is more severe than that of the original algorithm. The degree of unfairness for the SDMA-RT protocol parallels that of the SDMA protocol, but is consistently slightly lower.

To investigate further the nature of the unfairness intro- duced by the SDMA-RE variant, we show the per station

L. BametrKomputer Communications 21 (1998) 227-242 231

1 .o 2.0 3.0

Offered load

Fig. 15. Standard deviation of per station utilization versus offered load for the packet mixture with exponential arrivals.

0.010

$j 0.008

Z p s C 0.008 .g m iii

*ij 0.004

5 -0

8 0.002

Offered load

Fig. 16. Protocol fairness: standard deviation of per station utilization for SDMA variants with traffic consisting of 1526 byte packets.

utilization in Fig. 19. This plot is for the large packet traffic address stations exhibited by SDMA, it is clear from this load simulated at the crossover point of about 200% offered figure that stations are not provided fair access to the net- load. While there does not appear to be a consistent pattern work under these circumstances. The data indicate that such as the decrease in utilization from low-address to high- stations which are rightmost in a collision resolution interval

I I I s I ’ I ’ I

Offered load

Fig. 17. Protocol fairness: standard deviation of per station utilization for SDMA variants with traffic consisting of the packet mixture.

238

Fig. 18. Protocol fairness: standard deviation of per station utilization for SDMA variants with traffic consisting 76 byte packets.

L. BantettKomputer Communications 21 (1998) 227-242

Offered load

r

0.000 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Station number

Fig. 19. Per station utilization of SDMA-RE for 1526 byte packets at a load of approximately 200% of network capacity.

receive a smaller share of the capacity of the network than work to compensate for shorter bit times as the data rate other stations. increases.

4.3. Pet$omance at higher data rates

Given the trend towards higher data rates in LANs, we also considered the performance of the various protocols as

data rates increased. CSMA protocols require certain adjust-

ments as the data rate at which they operate increases in order to maintain the essential relationship between maximum propagation delay and minimum packet size. The two choices are to decrease the maximum extent of the network in proportion to the shrinking bit time, or to maintain the physical size of the network but increase the minimum allowed packet size so that the time to transmit still matches the unchanged propagation time. The 100 Mbps versions of Ethernet took the former approach. For this reason, the results discussed here also decrease the length of the net-

To isolate the effects of data rate increase, all other parameters were fixed to the extent possible. In particular,

the offered load was held as close as possible to 100% of capacity for the given data rate in all runs. Again, there were

two possible methods for maintaining the offered load level

as the data rate increased: increase the size of the packets

transmitted or increase the rate at which packets were transmitted while fixing the distribution of packet sizes. The

experiments reported here used the latter technique. Packet- size distribution depends primarily on the applications which make use of a network, not on the data rate of the network.

In summary, each data point presented in the following results reflects a change in three parameters: the maximum data rate of the network, the size of the network, and the rate at which stations generate packets. Other aspects of the simulation remained as described in Section 3.3.

L. BarnettKomputer Communications 21 (1998) 227-242 239

4.3.1. Average network utilization Figs. 20-22 show the average network utilization for

SDMA, the Capetanakis protocol and Ethernet for the

three packet-size distributions discussed in Section 3.3 as the maximum data rate of the network increases. The most striking aspect of these figures is the fact that the advantage

in throughput enjoyed by the collision resolution algorithms

at a maximum data rate of 10 Mbps is not sustained over the

range of maximum data rates simulated. In the case of

Fig. 20, the average throughput curves cross when the maximum data rate is approximately 30 Mbps, after which point

the average throughput is higher for Ethernet. This behavior is a result of the fact that, in order to maintain a.constant

offered load of approximately 100% of the capacity of the

network, the rate at which packets were generated was

scaled in proportion to the increase in the data rate for each set of levels simulated. For example, at 10 Mbps

using 76 byte packets, SDMA successfully transmitted

10273 packets per second, while Ethernet transmitted

8211 packets per second. With the data rate increased to 50 Mbps, SDMA transmitted 28 633 packets per second

and Ethernet transmitted 30485 packets per second. Given that the collision resolution algorithms cause packets to

bunch up waiting for the beginning of the next collision

resolution epoch to begin transmitting, an increase in the packet transmission rate translates to an increase in the

number of ready stations at the beginning of each epoch, more collisions necessary to resolve the epoch, and thus into

longer per packet delays. At 50 Mbps, fewer than 11% of packets transmitted by SDMA experienced fewer than four

collisions, while 74% of packets transmitted by Ethernet experienced fewer than four collisions. In fact, 42% of the

packets transmitted by Ethernet encounted no contention at

50 Mbps, while fewer than 1% of the SDMA packets were transmitted successfully on their first attempt.

Given that a traffic load consisting entirely of minimum- length packets is an endpoint which is not observed in

0.70

0.60 la0 -1

0.20 0 20 40 60 80 100

Max Data Rate (Mbps)

0.8 0 20 40 60 80 100


Fig. 20. Average network utilization versus maximum data rate, traffic Fig. 22. Average network utilization versus maximum data rate, traffic

consisting of 76 byte packets, network size decreased to maintain slot consisting of 1526 byte packets, network size decreased to maintain slot

size, load scaled to maintain approximately 100% utilization. size, load scaled to maintain approximately 100% utilization.

0.8 i I

= 0.7 - .s m 2

‘5 0.6 -

0.5 -

0 20 40 60 80 100


Fig. 21. Average network utilization versus maximum data rate, traffic

consisting of the packet mixture, network size decreased to maintain slot

size, load scaled to maintain approximately 100% utilization.

practice, it is interesting to compare the results of Fig. 20

with Fig. 2 1. Here, the situation is similar, but the crossover point for the curves has shifted further out the X axis, to a

maximum data rate of approximately 58 Mbps. So, for a more realistic mixture of packets, SDMA enjoys a perfor-

mance advantage over a wider range of data rates. It bears repeating that the packet mixture used in these simulations

has a mean packet size which is lower than other observed

mixtures (see Section 3.3). We would therefore expect that the crossover point for packet mixtures with larger mean

packet sizes would occur at even higher data rates. Fig. 22 lends weight to this hypothesis. This figure shows the aver-

age throughput for a traffic load composed of 1526 byte packets. Here, the curves do not cross over within the simu-

lated range of maximum data rates.

4.3.2. Average delay Figs. 23-25 show the average delay for SDMA, the Cape-

tanakis protocol and Ethernet for the three packet-size

240 L. BamettKomputer Communications 21 (1998) 227-242

1 .Oe-04

7.5e-05 al

2 2 9 5.0e-05 3 3

2.5e-05

0.0030

0.0025

0.0020 g g 0.0015 1

* 0.0010

0.0005

0.0000 t J

0 20 40 60 80 100 O.Oe+OO

0 20 40 60 60 100 Max Data Rate (Mbps)

Fig. 23. Average delay versus maximum data rate, traffic consisting of

76 byte packets, network size decreased to maintain slot size, load scaled

to maintain approximately 100% utilization.


Fig. 26. Delay variance versus maximum data rate, traffic consisting of



distributions discussed in Section 3.3 as the maximum data rate of the network increases. Average delay decreases as maximum data rate increases mainly because the actual transmission time of a packet is shorter at higher data rates. Because the size of the network is shrinking, collision duration is also shorter on average. As expected, the curves display the same crossover behavior as the throughput curves discussed in Section 4.3.1. As the data rate increases, the average delays for SDMA and the Capetanakis protocol converge. Results for the SDMA-RE protocol indicate that it maintains better average delay than Capetanakis over the data rates examined here. (These data were omitted from the figures to reduce clutter, since the results for the two variant protocols were consistent with those presented in Section 4 and provided no new insights.)

0.004

0.003

0.002

0.001

0.000 1 . n a a * ’ 0 20 40 60 80 100


Fig. 24. Average delay versus maximum data rate, traffic consisting of the

packet mixture, network size decreased to maintain slot size, load scaled to

maintain approximately 100% utilization.

4.3.3. Delay variance

Figs. 26-28 show the delay variance for the three packet- size distributions as the maximum data rate of the network

0.008

% 0.006 8 P 0” 0.004

0.002

0.000 t 1 0 20 40 60 80 100

3.0e-04

8 2.0e-04 E ‘C

J 3 6 l.Oe-04

O.Oe+OO 0 20 40 60 80

Max Data Rate (Mbps) Max Data Rate (Mbps)

Fig. 25. Average delay versus maximum data rate, traffic consisting of Fig. 27. Delay variance versus maximum data rate, traffic consisting of the

1526 byte packets, network size decreased to maintain slot size, load scaled packet mixture, network size decreased to maintain slot size, load scaled to

to maintain approximately 100% utilization. maintain approximately 100% utilization.

L. BamettKomputer Communications 21 (1998) 227-242 241

8 I ‘C

F

4.0e-04

P 5 P 2.0e-04

O.Oe+OO 0 20 40 60 80 100


Fig. 28. Delay variance versus maximum data rate, traffic consisting of



increases. The variance of delay for the CRAs decreases

slightly with increasing data rate, but there are no dramatic

changes. Ethernet, on the other hand, experiences a signifi-

cant decrease in the variability of delay as the data rate increases. As described in Section 4.3.2, this is probably due to the decrease in transmission time, the decrease in

network length and the related decrease in collision duration.

5. Conclusions

We have described three variants of the space division

multiple access protocol, a new collision resolution

algorithm. The performance of the original protocol and

the two variants was investigated through simulation. The

original protocol was compared with the simulated performance of Ethernet and an asynchronous version of the

Capetanakis tree protocol at a data rate of 10 Mbps under identical network conditions. SDMA was found to achieve a

higher average utilization and lower average delay under heavy load than either of the other protocols. The protocol

also achieved a significant improvement in the variance of delay versus Ethernet. SDMA’s performance advantage

over Ethernet holds in essentially any situation where contention occurs at the 10 Mbps data rate.

The original protocol was shown to be biased in favor of

stations with low addresses. However, comparison of indi-

vidual station performance under the same network layout and traffic conditions showed that this bias was less severe

than a similar location bias in the Ethernet protocol. We

conclude that the location bias, being no worse than that present in a widely deployed protocol, should not be a ser- ious impediment to the use of SDMA.

The SDMA-RE variant was designed to counteract the location bias experienced by stations using the original SDMA protocol. The design was successful for a wide range of traffic loads in the load region most likely to be

of interest in real networks. The algorithm introduces its

own pattern of unfairness, but this unfairness manifests

itself at much higher offered loads than the problem with

the original SDMA. The technique used in the SDMA-RT variant could be

used to reduce the size of the set of stations participating in

the idle marking collision for any CRA which uses unique

addresses as the criterion for subdividing an interval. How-

ever, the performance benefit demonstrated for SDMA-RT

is a direct result of the correspondence between address and

physical location assumed by SDMA. On the other hand, the

“relaxed entry” technique is applicable to any collision

resolution algorithm which has the property that stations which have transmitted in the current collision resolution

epoch are never re-enabled within the same epoch.

The protocols were also compared at higher data rates

with offered load approximately equal to the capacity of

the network. In these experiments, SDMA was shown to have better performance than Ethernet in most interesting

situations. Ethernet had higher utilization for traffic loads

with a predominance of small packets at higher data rates.

Acknowledgements

I wish to thank Arthur Charlesworth, Joseph F. Kent and Brian Whetten for careful proofreading of this paper and

helpful comments regarding its content,

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