Download - Waiting Line Management
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.