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Waiting Line Management. Chapter #12. Waiting Line. See Page # 291 (Book-1). 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.

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Waiting line
Waiting Line

See Page # 291 (Book-1)

  • One or more ‘customers’ waiting for a service.

  • ‘Customer’ can be:

    • Peoplee.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.

Why waiting lines form
Why waiting lines form?

  • 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

Effects of waiting line
Effects of Waiting Line

  • 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.

Objectives of waiting line analysis
Objectives of Waiting Line Analysis

  • To improve system Utilization

  • To minimize the sum of two costs

    • Customer waiting costs

    • Service capacity costs

Structure of waiting line problems
Structure of Waiting-Line Problems

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

  • A waiting line of customers. (Customers Behavior)

  • 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.

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

Customer population

Service system

Served customers

Waiting line

Service facilities

Priority rule

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

Customer population or input



Customer Population or Input

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 an infinite source do not affect the probability of another arrival

  • Customers from a finite source reduce the chance of new arrivals

Customer behavior
Customer Behavior

  • 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.

The service system
The Service System

  • 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 customer



Service time for customer



Example: Items coming down an automated assembly line.

Example: People spending time shopping.

No of lines in system

Service facilities

(a) Single line

Service facilities

(b) Multiple lines

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 system arrangement
Service system Arrangement

  • Single-channel, single-phase

  • Single-channel, multiple-phase

  • Multiple-channel, single-phase

  • Multiple-channel, multiple-phase

  • Mixed arrangement

Service facility

Service facility 1

Service facility 2

(a) Single channel, single phase

(b) Single channel, multiple phase

Examples of Service Facility Arrangements

Service facility 1

Service facility 1

Service facility 3

Service facility 2

Service facility 2

Service facility 4

(c) Multiple channel, single phase

(d) Multiple channel, multiple phase

Routing for : 1–2–4

Routing for : 2–4–3

Routing for : 3–2–1–4

Service facility 1

Service facility 2

Service facility 3

Service facility 4

(e) Mixed arrangement

System arrangement examples


barber shop/ATM use

Car wash

Bank tellers’




System Arrangement examples

Single Phase


Single Channel


Priority rule for waiting line
Priority Rule for waiting line

  • 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.

Important measures of waiting line analysis
Important Measures of Waiting line Analysis

  • 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

Decision areas for management to avoid waiting lines
Decision Areas for Management to avoid waiting lines

  • Arrival rates

  • Line arrangement

  • Number of service facilities

  • Number of phases

  • Number of servers per facility

  • Server efficiency

  • Priority rule

Strategies for waiting line management
Strategies for Waiting line management

  • 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.