One or more ‘customers’ waiting for a service.

‘Customer’ can be:› People e.g. A person waiting in line to deposit

cash in a bank.› Objects e.g. A machine waiting for

maintenance, Inventory waiting to be delivered. Truck waiting to be loaded etc.

See Page # 291 (Book-1)

Temporary imbalance between demand and capacity.

Larger arrival rate than servicing rate Randomness/Variability

Customers usually arrive at random intervals Variability in order lengths – some orders

take longer than others

Waiting lines are non-value added occurrences. Waiting in lines does not add enjoyment for

customers. Waiting in lines does not generate revenue for

company. Costly to provide additional waiting space. Possible loss of business.

› Customers refusing to wait› Customers leaving

Loss of customer goodwill. Reduction in customer satisfaction. Congestion may disrupt other business operations.

To improve system Utilization

To minimize the sum of two costs› Customer waiting costs› Service capacity costs

1. An input, or customer population, that generates potential customers.

2. A waiting line of customers. (Customers Behavior)

3. The service facility, consisting of a person (or crew), a machine (or group of machines), or both necessary to perform the service for the customer.

4. A priority rule, which selects the next customer to be served by the service facility.

Customer population

Service system

Waiting line

Priority rule

Service facilities

Served customers

Figure C.1 – Basic Elements of Waiting-Line Models

Population Source

Example: Number of machines needing repair when a company only has three machines.

Example: The number of people who could wait in a line for gasoline.

Customers from a finite source reduce the chance of new arrivals

Customers from an infinite source do not affect the probability of

another arrival

Customers are patient or impatient

Patient customers wait until served

Impatient customer behave in different ways:

Balking: When customer decides not to enter in line.

Jockeying: When customer switches to another line.

Reneging: When customer quits waiting and leaves the line.

Service rate depends on the structure of service system and facility.

Structure of a service system depends on various factors such as:

› Service time for customer› No. of lines› No. of service channels› No. of service phases

Service time for customerServiceTimes

Constant Variable

Example: Items coming down an automated assembly line.

Example: People spending time shopping.

No. of lines in system› A single-line keeps servers uniformly busy and levels

waiting times among customers › A multiple-line arrangement is favored when servers

provide a limited set of services

Service facilities

(a) Single line

Service facilities

(b) Multiple lines

Single-channel, single-phaseSingle-channel, multiple-phaseMultiple-channel, single-phaseMultiple-channel, multiple-phaseMixed arrangement

Service facility

(a) Single channel, single phase

(b) Single channel, multiple phase

Service facility 1

Service facility 2

Examples of Service Facility Arrangements

(c) Multiple channel, single phase

Service facility 1

Service facility 2

Service facility 3

Service facility 4

Service facility 1

Service facility 2

(d) Multiple channel, multiple phase

Routing for : 1–2–4Routing for : 2–4–3Routing for : 3–2–1–4

(e) Mixed arrangement

Service facility 1

Service facility 4

Service facility 3

Service facility 2

Single Channel

Multichannel

Single Phase Multiphase

First-come, first-served (FCFS)—used by most service systems

Earlier Due Date (EDD) Shortest Processing Time (SPT) Preemptive discipline—allows a

higher priority customer to interrupt the service of another customer or be served ahead of another.

System Utilization Average Number of Customers

Waiting Average Customer Time in System

› Waiting time + processing time Average Customer Waiting Time

› Typically, you don’t want to keep the customer waiting for an unreasonable amount of time

Customer Waiting Costs Service Costs Probability of Lost Sales

› Would like to minimize

1. Arrival rates2. Line arrangement 3. Number of service facilities4. Number of phases5. Number of servers per facility6. Server efficiency7. Priority rule

Reduce perceived waiting time› Tell customers how long their wait will be› Magazines in waiting rooms› Music/television› In-flight movies› Filling out forms

Derive benefits from waiting› Place impulse items in service facility› Advertise other goods/services› Encourage customers to come during the

slack periods.