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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.