IEEE TRANSACTIONS ON COMPUTERS, VOL. c-32, NO. 12, DECEMBER 1983

Two-Level Replacement Decisions in PagingStores

OZALP BABAOGLU, MEMBER, IEEE, AND DOMENICO FERRARI, SENIOR MEMBER, IEEE

Abstract-One of the primary motivations for implementing virtualmemory is its ability to automatically manage a hierarchy of storagesystems with different characteristics. The composite system behavesas if it were a single-level system having the more desirable charac-teristics of each of its constituent levels. In this paper we extend thevirtual memory concept to within the top level of a two-level hierarchy.Here, the top level is thought of as containing two additional levelswithin it. This hierarchy is not a physical one, but rather an artificialone arising from the employment of two different replacement algo-rithms. Given two replacement algorithms, one of which has goodperformance but high implementation cost and the other poor per-formance but low implementation cost, we propose and analyzeschemes that result in an overall algorithm having the performancecharacteristics of the former and the cost characteristics of the latter.We discuss the suitability of such schemes in the management ofstorage hierarchies that lack page reference bits.

Index Terms-FIFO, LRU, Markov chain, page replacement al-gorithms, UNIX, VAX VMS, virtual memory, working set.

I. INTRODUCTION

E CONOMIC realities force the construction of large vir-tual address spaces in the form of hierarchies. A typical

two-level hierarchy consists of a fast, expensive, and small (thelatter two being a consequence of the first attribute) primarymemory in addition to a slow, cheap, and large secondarymemory. Obtaining the appearance of a single level that is fastand large by the automatic management of the hierarchy isprobably one of the primary motivations for incorporatingvirtual memory in a computer system [15], [17].

Every level except the last (i.e., the slowest) in a hierarchyadopts a replacement policy to remove data down to the nextlevel when necessary. The topic of replacement algorithms thatare suitable for such environments has been the subject of alarge number of investigations [23]. Specifically, the virtualmemory system we are concerned with employs demandpaging [12]. The replacement algorithms that have beenproposed for this environment can be crudely classified as beingeither inexpensive to implement but having poor performance,

Manuscript received August 27, 1982; revised February 25, 1983, and June3, 1983. This work was supported in part by the National Science Foundationunder Grant MCS78-246 18. The work of 0. Babaoglu was supported by theItalian National Research Council through a Fellowship for ForeignScholars.

0. Babaoglu was with the University of California, Berkeley, CA. He isnow with the Department of Computer Science, Cornell University, Ithaca,NY 14853.

D. Ferrari is with the Computer Science Division, Department of ElectricalEngineering and Computer Sciences, University of California, Berkeley, CA94720.

or being expensive to implement but having better perfor-mance. Our informal notion of cost of implementation con--siders factors such as hardware support other than the basicaddress translation mechanism and the complexity of the as-sociated software. Our criterion for performance, on the otherhand, is based on the frequency of page faults. Examples ofreplacement algorithms of the cheap-to-implement-but-poor-performance type include the First-In-First-Out (FIFO)and the Random (RAND) algorithms [7]. The Least RecentlyUsed (LRU) [19] and the Working Set (WS) [1 1] algorithms,on the other hand, are examples of the expensive-to-imple-ment-but-good-performance class.

In the next few sections, we introduce a class of hybrid re-placement policies that combine two algorithms, one of eachof the above categories, within a single level of the physicalstorage hierarchy. After deriving expressions for their per-formance, we demonstrate that these algorithms, in fact,achieve performances close to those of LRU and WS whilehaving implementation costs comparable to those of FIFO andRAND. The next section introduces the program model onwhich our analyses will be based.

II. THE INDEPENDENT REFERENCE MODEL

The mathematical analysis of a replacement algorithm re-quires a model of the programs on which the policy operates.For our purposes, an execution of a program consisting of npages labeled 1, 2, *.. , n) results in a page reference string,r1, r2, r3, * , rt_, rt, rt+i, * * where ri = i if page i is ref-erenced at time instant t (memory references are assumed tooccur at equidistant time points, and we define their distanceto be the unit of time). We will assume a particularly simplestochastic structure for the reference string, known as the In-dependent Reference Model (IRM) [ 1 ]. As the name implies,the string $ri; i = 1, 2, * is assumed to be a sequence of in-dependent identically distributed random variables from thepopulation {1, 2, * nl where Pr(rt = i) = /i for all t andn

Li= 1.i=l

Modeling an actual program with the IRM involves ob-taining point estimates for the model parameters (/3's) thatare simply the frequency counts of pages in an actual referencestring generated by the program. Baskett and Rafii haveproposed an alternate method for obtaining estimates for the/i's, called the AO Inversion Model [6]. The resulting model,although structurally identical to the IRM, has much better

0018-9340/83/1200-1151$01.00 ©) 1983 IEEE

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predictive capabilities for the performance of real pro-grams.

III. HYBRID POLICIES

In a demand-paged virtual memory system, referencing apage that is invalid-not in main memory-causes a trap,which is known as a pagefault. We note that, even in the ab-sence of any additional hardware support to maintain referencebits, this address translation mechanism can be put to use todetect references to pages that are already in memory. All thatis required is that we be able to distinguish these faults fromnormal page faults and refrain from initiating the I/O oper-ation. This special state of a page will be called the reclaimablestate, and will be identified by one additional bit in each pagetable entry. Since this method of detecting references to pagescomes at a cost (to be discussed later), we are interested inreplacement algorithms that collect reference information onlyfor a subset of the pages that a program has in memory. Moreformally, we have partitioned the set of pages in memory intotwo disjoint classes, {valid} and freclaimablel, such that

{memoryl = {valid} u {reclaimablel and{valid} n freclaimable} = 4.

To keep the cost of generating spurious faults to the rec-laimable pages at reasonably low levels, we would like tohave

I Ireclaimablel I

BABAOGLU AND FERRARI: TWO-LEVEL REPLACEMENT DECISIONS

by an m-tuple (without repetitions) corresponding to thememory control state of the policy. The first k entries of scontain the page names that constitute T, whereas the re-maining m - k entries contain the names of the elements ofB. Define the Markov chain [Xt, t = 0, 1, * - }, with Xt = s ifthe memory control state at time t is given by s. Let Q = Is)denote the state space of this Markov chain.The one-step transition probabilities denoted by

p(s, s') = Pr(Xt = s'lXt-I = s), t > 1can be determined easily based on the IRM parameters and.on the algorithm's description. Specifically, for HFIFO-LRU,

kFL iiii=l0jig

if s' = s

ifkS

IEEE TRANSACTIONS ON COMPUTERS, VOL. C-32, NO. 12, DECEMBER 1983

kZ liji, if s' = si=1

/3j/k, if s' = [1jlJ2 * *jh-ljh+ I... jkJhik+1 * * *Jm-I]p(s,Ss) = wherejt sandi

BABAOGLU AND FERRARI: TWO-LEVEL REPLACEMENT DECISIONS

Theorem 3: The steady-state fault rate for the HFIFO-WSpolicy with parameters k and T is given by

n

F(HFIFO-WS) = 1 - EZ 3i j7i + (1 - i)i=1

E ri(i riv- E pli0)p, Pi) 1]where r1r, Fi, and Pi are as defined in Lemma 3.

Proof: In steady state, the probability that page i causesa fault is simply the steady-state probability that it is not inmemory and is referenced. Thus, conditioning on the page,

F(HFIFO-WS) = (1 - Pr(i e {memory})) *3i.i=I

The result then follows trivially upon the substitution of (5)into the above expression. I3

Theorem 4: The mean memory occupancy due to theHFIFO-WS POiCY with parameters k and T is given by

M(IJFIFO-WS) = E i + (1 -i

where Wri, F,, and Pi are as defined as Lemma 3.Proof: Conditioning on the page, we have

nM(HFMFOws) = L Pr(i E {memory3).1=1

The result follows imnmediately from the substitution of(S) intothe above expression. o

2) The RAND-AWS Hybrid Policy: Here, we consider avariation of the HFIFO-WS policy that operates exactly as de-scribed in the previous section except that, at the times ofevents, the page to leave the top is selected at random uni-formly over the pages currently in T.

Theorem 5: The steady-state fault rates and the measnmemory occupancies for the HRANi WS policy are identicalto those of theHFFo-Ws policy with the same parameters.

Proof: Bay Lemma 2 we know that the equilibriumprobabilities for the Markov chain states are the same for boththe RAND and the FIFO policies. Also, by Corollary 3, weknow that the two policies-result in the same steady-state faultrate. Based on these observations, the proof followstrivially. a

IV. NUMERICAL RESULTS

To study the behavior of the F(HFIFO-LRu(k)) functionbetween the two end points corresponding to pure LRU andpure FIFO fault rates, we computed numerical values of theexpression given in (3) for various choices of the IRM pa-rameters. To minimize the number of parameters involved, thetwo instances of the IRM we consider were generated throughthe equations fi = ci and fi = ci, which are called the arith-metic and the geometric models, respectively. In both cases,

nthe constant c is chosen such that -E f3' = 1. In Fig. 1,

i=l

Arithmetic IRM

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-

0Ir.a

cu' .Ud I I I -r I In=8nm=7.08 /.07 _.06 -

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Top Size A (pages)(a)

Geometric IRMnP.

0I

0

Ca.

.015

.011

1 2 3 4 5 6 7 8

Top Size 4 (pages)(b)

Fig. 1. HFIFO-LRU and HRAND-LRU fault rates for two sample programsas a function of the policy parameter k.

F(HFIFO-LRu(k)) is plotted as a function of k for the fixedvalues n = 8 and m = 7. Note the strong convexity of the twocurves; particularly the one corresponding to the geometricIRM, where fault rates that are practically identical to the pureLRU fault rate are achieved even for top sizes of 5 pages (orequivalently, bottom sizes of 2 pages). Outside of the uniformIRM case- (i.e., fli = 1/n for all i), the strict convexity ofF(HFIFO-LRU(k)) as a function k for all m and IRM param-eter values remains a conjecture.

The above results have to be interpreted with caution for tworeasons.

1) They are based on a model of program behavior that isknown to lack many of the properties of real programs.

2) Due to the factorial growth of the complexity of theexpressions involved, numerical results can only be presentedfor unrealistically small values of the program size n and of thememory size m.

I

n=8m=7

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IEEE TRANSACTIONS ON COMPUTERS, VOL. C-32, NO. 12, DECEMBER 1983

To eliminate these concerns, trace-driven simulations of thehybrid policies were carried out using three program samplescalledcWATFIV, APL, and FFT consisting of 96, 114, and 82pages, respectively. The page size for the WATFIV programis 1024 bytes, whereas the APL and FFT program page sizeis 512 bytes. The reader should consult [22] for further detailsabout the programs. The resulting values of th, fixed partitionhybrid fault rates as a function of the policy parameter aredisplayed in Fig. 2. These curves indicate that the conclusionsbased on analytic results are also valid for the three programsavailable to us. All three programs display a strongly convexcurve with a well-defined knee at approximately k = 40 pages.Note that this represents a bottom size of 10 pages or, equiv-alently, 20 percent of the total memory size. This observationis npt due to an anomaly of the three sample programs and thepatrticular parameter values but is a more general property ofthe hyrid policies. If the pure LRU fault rate of a program wereto remain relatively constant for memory sizes greater than10 pages, there would be little incentive to add 40 more pagesto the memory no matter how inexpensive their managementwas. However, from the data presented in [22], we observe thatthe pure LRU fault rates for these programs continue to de-crease and do not flatten out for memory sizes greater than 10pages,We also note that the HFIFO-LRU and HRAND-LRU policies

result in different fault rates for these programs. This confirmsthe fact that these progranms do not satisfy the IRM assump-tions. No general conclusion about the relative performaicesof the HFIFO-LRU and HRAND-LRU policies however, can bederived from these results, as each is upiformly superior forone of the programs, while both perform about the same forthe remaining program.

V. COST CONSIDERATIONSUp to this point, the only performance measure we have

been concerned with has been the steady-state fault rate as afunction of the mean memory occupancy. The operation oftbese hybrid policies requires setting the policy parameter kto some value. If the cost of referencing a page'that is in B werenegligible, then setting k = I would almost always producepptimum performance with respect to the page'fault rate (thereare few points in the graphs of Fig. 2 where the fault rate ac-tually drops as k is increased beyond 1). However, since a finitecost is incurred each time a page in B is referenced, -the selec-tion of the policy-parameter should be guided by the desire tokeep the fault rate close to the value given by pure LRU al-gorithm while minimizing the size of B (i.e., minimizing therate of reclaims). Tntuitively, the policy should be operated withthe parameter set to a value close to the knee that occurs in allthree fault rate graphs. Formally, we define a performancemeasure C(), that is'the weighted sum of the fault'rate and thereclaim rate for a given value of the pQlicy parameter. For apage replacement algorithm A and a ratio of page fault servicetime to page reclaim service time given by a, let

C(A,m,k,oa) =f(A,m - k) + a F(A,m,k)where m is the memory size, k is the policy parameter (or thesize of T) andf(-) is the reclaim rate. Note that while appro-

.0005

C144

-0 .0004

0

0 .0003

IIIIII T .T T-TT-

WATFIVm=50 panes-. - -- r -o--

iI

~~~~~H~~~~~RD-LRU j/

INII I

IiL ii1 WiI.I I.tIII IIIIII ILI I il1 II III III II10 20 30 40 50

Top Size & (pages)(a)

Top Size (pages)(b)

Top Size (pages)(c)

Fig. 2. HFIFO-LRU and HRAND-LRU fault rates as a function of the policyparameter k for (a) WATFIV, (b) APL, and (c) FFT.

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BABAOGLU AND FERRARI: TWO-LEVEL REPLACEMENT DECISIONS

priate as a responsiveness measure from the point of view ofan individual program, the cost function CQ) is inappropriatefor multiprogramming system throughput considerations sincethe major part of the delay due to a page fault results from thepaging I/O operation, which can be overlapped with otherCPU activity. On the other hand, a reclaim operation is per-formed entirely by the CPU and cannot be overlapped.Due to the complexity of the expressions for the steady-state

fault and reclaim rates, an analytic minimization of the costfunction defined with respect to k cannot be carried out. Asbefore, we resort to trace-driven simulation to study the be-havior of this cost function as the policy parameter changes.Fig. 3 displays this cost function for the three programs underthe HFIFO-LRU policy. For the sake of brevity, we restrict thepresentation of the results to the case a = 100 under theHFIFO-LRU policy. Our conclusions, however, are applicableto the HRAND-LRU policy as well as to the cases when a = 10and a = 1000 under both policies. The particular choice of thevalue of a for the results reported here is further supported bymeasurements from an actual system [4]. As can be seen inFig. 3, the optimum setting for the policy parameter k variessignificantly depending on the program as well as on the totalamount of memory allocated to it. In [24], Turner and Levyreport on the behavior of this cost function for different valuesof a. The observed insensitivity of the optimum value of thepolicy parameter to variations of a is unfortunately not veryvaluable since, for a given implementation, a tends to be ratherstatic anyway. In a real system, the characteristics of the dif-ferent programs and the amount of metnory allocated to eachprogram are far more dynamic. Our results demonstrate thatit is precisely these variations that require the parameter to beadjusted for the hybrid policies to perform optimally. Condi-tions which make m a variable rather than a fixed system pa-rameter are discussed in the next section.

Fig. 4 compares the performance of the two variable parti-tion hybrids to that of the fixed partition hybrid. For the threeprograms studied, the HFIFO-WS and HRAND-WS policies havesimilar performances, with neither exhibiting uniform supe-riority. This is not surprising after our observation of the FIFOand RAND policies in conjunction with the LRtJ bottom. Bothof these variable partition policies, however, outperform thefixed partition hybrids (by more than an order of magnitudein some cases) for equal values of the parameter and of themean memory size in all three programs. Furthermore, thesevariable partition hybrids tend to have performances that aremore uniform with respect to changes in the memory size thantheir fixed partition counterparts. Note that Fig. 4(c) containsmean memory sizes that are less than the parameter value forthe case k = 50. This results from the fact that our simulationstudies assume an empty initial memory that may take a longtime to fill.

VI. EXTENSIONSIn a multiprogramming environment, the fixed partition

hybrids can be extended in a natural way to operate asFIFO-Global LRU and RAND-Global LRU hybrids, thusresulting in variable partitions for the individual programs.This can be accomplished simply by maintaining a single fixed

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Fig. 3. The weighted sum cost observed under the HFIFO-LRU policy forvarying amounts of memory as a function of the policy parameter andprograms (a) WATFIV, (b) APL, and (c) FFT.

WATFIVa=100

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IEEE TRkNSACTIONS ON COMPUTERS, VOL. c-32, NO. 12. DECEMBER 1983

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HFIFO-LRU (lines), HFIFoWS, and HRAND.WS policy weighted sum costs as a function of the memory size m for (a) WATFIV,(b) APL, and (c) FFT'. The window size T was varied between 1730 and 1 17300 refetences to obtain the variable partition results.Key: 0, &, and v represent HFIFO-WS with k = 10, 30, 50, respectively, whereas 0, 0, and @ represent HRAND-WS with k =10, 30, 50, respectively.

size bottom containing the reclaimable pages of all the pro-grams that are currently being multiprogrammed (the tops foreach of the programs, however, are still maintained sepa-rately). In such an environment, the total number of pageframes allocated to a program at any given time will be the sizeof its top plus a random variable that represents the numberof pages in B belonging to the given program. Under this ex-tension, the study of the performance of individual programsis severely complicated due to their interactions with the otherconcurrently running programs.

Although we have not studied it analytically, we note thatthis extension of the HFIFO-LRU policy adequately models thememory management policy employed in the VMS operatingsystem for the VAX-1l1/780 computer system [110], [24], [18].Unfortunately, for optimality to be preserved under this ex-tension, not only must the hybrid policy parameter be set ona per-program basis, but it should also vary dynamically as theamount of memory allocated to the program changes. We note

that heuristics such as those that try to keep the top size to thebottom size ratio a constant or that try to maintain a constantreclaim rate can be employed to vary the policy parameterdynamically. The current version of VMS, in fact, implementsa scheme similar to the second option to adjust the size ofT aseach program executes [24]. In [4], Babaoglu and Joy presenta considerably different approach to the page replacementproblem in an architecture lacking reference bits that wasimplemented as part of the Berkeley UNIX' operatingsystem.

VII. CONCLUSIONS

We have introduced a class of hybrid algorithms that areguitable for page replacement decisions in hierarchical storesthat lack hardware support other than the address translation

UNIX is a trademark of Bell Laboratories.

APLa=100

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BABAO6LU AND FERRARI: TWO-LEVEL REPLACEMENT DECISIONS

mechanism. Expressions for the steady-state fault rates gen-erated by these policies have been derived based on the Inde-pendent Reference Model of program behavior. With theappropriate setting of the policy parameter, numerical andempirical results suggest that these algorithms are capable ofachieving fault rates close to those of the pure LRU and WSpolicies while incurring costs comparable to those of the FIFOand RAND policies.We have defined a cost function that includes explicitly, the

cost of reclaim operations; this function is more suitable thanthe simple fault rate for the evaluation of hybrid algorithms.Based on this cost function, the parameter of the hybrid policieswe analyzed was seen to be sensitive to variations in the pro-gram characteristics as well as to the amount of memory al-located to it. We have suggested reasonable heuristics that canbe incorporated into these policies to allow the dynamic ad-justment of their parameters.

REFERENCES

[1] A. V. Aho, P. J. Denning, and J. D. Ullman, "Principles of optimal pagereplacement," J. Ass. Comput. Mach., vol. 18, pp. 80-93, Jan. 1971.

[2] 0. 1. Aven, L. B. Boguslavsky, and Y. A. Kogan, "Some results on dis-tribution-free analysis of paging algorithms," IEEE Trans. Comput.,vol. C-25, pp. 737-745, July 1976.

[3] 0. Babaoglu, "Virtual storage management in the absence of referencebits," Ph.D. dissertation, Univ. of California, Berkeley, Memo ERLM81/92, Nov. 1981.

[4] 0. Babaoglu and W. N. Joy, "Converting a swap-based system to dopaging in an architecture lacking page-referenced bits," in Proc. 8thSymp. Operating Syst. Principles, SIGOPS, Dec. 1981, pp. 78-86.

[5] 0. Babaoglu, "Hierarchical replacement decisions in hierarchicalstores," in Proc. ACM SIGMETRICS Conf Measurement and Mod-eling Comput. Syst., Aug. 1982, pp. 11 - 19; also in Performance Eval.Rev., Winter 1982-1983.

[6] F. Baskett and A. Rafii, "The Ao inversion model of program pagingbehavior," Dep. Comput. Sci., Stanford Univ., Rep. STAN-CS-76-579,Oct. 1976.

[7] L. A. Belady, "A study of replacement algorithms for a virtual storagecomputer," IBM Syst. J., vol. 5, pp. 78-101, 1966.

[8] E. G. Coffman and P. J. Denning, Operating Systems Theory. En-glewood Cliffs, NJ: Prentice-Hall, 1973.

[9] F. J. Corbato, "A paging experiment with the multics system," MIT,Cambridge, MA, Project MAC Memo. MAC-M-384, July 1968. Alsoin In Honor of P. M. Morse ed. Cambridge, MA: Ingard MIT Press,1969, pp. 217-228.

[10] VAX-11/78OSoftware Handbook. Bedford, MA: Digital, 1978.[11 P. J. Denning, "The working set model of program behavior," Commun.

Ass. Comput. Mach., vol. I1, pp, 323-333, May 1968.[12] , "Virtual memory," Comput. Surveys, vol. 2, no. 3, pp. 153-189,

Sept. 1970.[13] M. Easton and P. A. Franaszek, "Use bit scanning in replacement de-

cisions," IEEE Trans. Comput., vol. C-28, pp. 133-141, Feb. 1979.[14] M. H. Fogel, "The VMOS paging algorithm-A practical implemen-

tation of a working set model," Oper. Syst. Rev., vol. 8, pp. 8-17, Jan.1974.

[15] J. Fotheringham, "Dynamic storage allocation in the Atlas computerincluding an automatic use of backing store," Commun. Ass. Comput.Mach., vol. 4, pp. 435-436, Oct. 1961.

[16] E. Gelenbe, "A unified approach to the evaluation of a class of re-placement algorithms," IEEE Trans. Comput., vol. C-22, pp. 611-618,June 1973.

[17] T. Kilburn, D.B.G. Edwards, M. J. Lanigan, and F. H. Sumner, "Onelevel storage systems," IRE Trans. Electron. Comput., vol. EC-I 1, pp.223-235, Apr. 1962.

[18] E. D. Lazowska, "The benchmarking, tuning and analytical modelingof VAX/VMS," in Proc. Conf. Simulation, Measurement and Mod-eling Comput. Syst., Boulder, CO, Aug. 1979, pp. 57-64.

[19] R. L. Mattson, J. Gecsei, D. R. Slutz, and 1. L. Traiger, "Evaluationtechniques for storage hierarchies," IBM Syst. J., vol. 9, pp. 78-117,1970.

[20] B. G. Prieve, "A page partition replacement algorithm," Ph.D. disser-tation, Univ. California, Berkeley, 1974.

[21] S. M. Ross, Applied Probability Models with Optimization Applica-tions. San Francisco: Holden-Day, 1970.

[22] A. J. Smith, "Two simple methods for the efficient analysis of memoryaddress trace data," IEEE Trans. Software Eng., vol. SE-3, pp. 94-101,Jan. 1977.

[23] , "Bibliography on paging and related topics," Oper. Syst. Rev.,vol. 12, no. 4, pp. 39-56, Oct. 1978.

[24] R. Turner and H. Levy, "Segmented FIFO page replacement," in Proc.ACM SIGMETRICS Conf Measurement and Modeling Comput.Syst., Sept. 1981, pp. 48-51; also in Performance Eval. Rev., Fall1981.

_Ozalp Babaoglu (S'78-M'8 1) was born in Ankara,Turkey, in 1955. He received the B.Sc. degree inelectrical engineering from George WashingtonUniversity, Washington, DC, in 1976 and theM.Sc. and Ph.D. degrees in computer science fromthe University of California, Berkeley, in 1977 and1981, respectively.He spent the summer of 1978 at IBM San Jose

Research Laboratory as an Academic Associateand the first half of 1980 as a Foreign Scholar at

the Numerical Analysis Institute of the Italian National Research Councilin Pavia, Italy. Before joining the faculty at Cornell University, Ithaca, NY,in 1981 as an Assistant Professor, he was a Staff Scientist with the ComputerScience and Applied Math Group, Lawrence Berkeley Laboratories, Berkeley,CA. He was the principal designer and coimplementor of the virtual memoryextensions to the UNIX operating system, known as 3.Obsd, for the VAXcomputer. He was the corecipient of the 1982 Sakrison Memorial Award forhis contributions to the Berkeley UNIX operating system. His current researchinterests include performance evaluation, modeling, and distributed andfault-tolerant computing systems.

Dr. Babaoglu is a member of the Association for Computing Machineryand the IEEE Computer Society.

.I II 1, Domenico Ferrari (M'67-SM'83) received theDr.lng. degree in electronic engineering from thePolytechnic Institute of Milan, Italy, in 1963.

_ In 1964, he joined the Computer Laboratory,Polytechnic Institute of Milan, and started doing

g research in switching theory, high-speed arithme-tic units, logical design, and later in computer-aided electronic circuit design. He became an Ass-itant Professor in 1967, and was awarded the Lib-era Docenza in computer science in 1969. In 1970,he joined the faculty of the Department of

Electrical Engineering and Computer Sciences, University of California,Berkeley, where he is now Professor of Computer Science. Since then, he hasbeen academically and professionally involved in computer systems perfor-mance evaluation activities, with particular emphasis on instrumentationdesign, virtual-memory system improvement, and workload characterization.His more recent interests include program behavior modeling, computersystems dynamics, and distributed system performance measurement andevaluation. From 1970 to 1973, he participated in the development of PRIME,an interactive multiprocessor system designed by the Computer SystemsResearch Project of the University of California with ARPA support. Since1974, he has directed the PROGRESS Group, which does research in per-formance evaluation with the support of the National Science Foundation.

Dr. Ferrari has organized conferences and advanced courses, lectured ex-tensively in the U.S. and in Europe, and consulted for EDP centers, universityinstallations, computer manufacturers, and software houses in the areas ofperformance improvement and capacity planning. He is the author of Com-puter Systems Performance Evaluation, Prentice-Hall, 1978, a coauthor ofMeasurement and Tuning of Computer Systems, Prentice-Hall, 1983, theeditor of Performance of Computer Installations-Evaluation and Man-agement (North-Holland, 1978) and a coeditor of Experimental ComputerPerformance Evaluation North-Holland, 1981, as well as of Theory andPractice ofSoftware Technology, North-Holland, 1983. He is on the Inter-national Board of Editors of Performance Evaluation, and is a member of theACM and of the IEEE Computer Society.