OM-10&11-Chapter 18 Management of Waiting lines

Waiting Lines

Occur in all sorts of service systems, wait time is non-value added.
Wait time ranges from acceptable to the emergent:
short wait in drive thru, sitting in an airport waiting for delayed flight, waiting for emergency service personnel
Wait time costs:
Low

Queuing Theory

Mathematical approach to the analysis of waiting lines
Applicable to many environments:
-call centers, banks, post offices, restaurants, theme parks, telecommunication systems, traffic management

Why is there waiting?

Waiting lines tend to form when a system is not fully loaded
Variability- arrival and service rates are variable
Services cannot be completed ahead of time and stored for use later

Managerial implications: why waiting lines cause concern

1) The cost to provide waiting space
2) A possible loss of business when customers leave the line before being served to refuse to wait at all
3) a possible loss of goodwill
4) A possible reduction in customer satisfaction
5) Resulting congestion may disr

Waiting line management

The goal of waiting line management is to minimize total costs:
Costs associated with customers waiting for service and capacity cost

Waiting line characteristics

1) Population source
2) Number of servers (channels)
3) Arrival and service patterns
4) Queue discipline

Population source: infinite/ finite

Infinite source: customer arrivals are unrestricted, the number of potential customers greatly exceeds system capacity
Finite source: The number of potential customers is limited

Channel and Phases

Channel: A server in a system, it is assumed that each channel can handle one customer at a time
Phases: The number of steps in a queuing system

Common Queuing Systems

Single Channel, single phase
Single channel, multiple phase
Multiple channel, single phase
Multiple channel, multiple phase

Arrival Patterns

Arrival Pattern:
Most commonly used models assume the arrival rate can be described by the Poisson distribution
-arrivals per unit of time
Equivalently, interarrival times are assumed to follow the negative exponential distribution
-the time between arriv

Service pattern

Service times are frequently assume to follow a negative exponential distribution

Queue Discipline

The order in which customers are processed
Most commonly encountered rule is that servie is provided on a first come, first serve basis
Non first come first serve applications do not treat customer waiting costs as the same

Waiting line metrics

Managers typically consider 5 measures when evaluating waiting line performance:
1) the avg number of customers waiting (in line or in the system)
2) the avg time customers wait (in line or in the system)
3) System utilization
4) The implied cost of a giv

Waiting line performance

The avg number waiting in line and the avg time customers wait in line increase exponentially as the system utilization increases

4 basic infinite source models

All assume a poisson arrival rate
1) single server, exponential service time
2) single server, constant service time
3) multiple servers, exponential service time
4) Multiple priority service, exponential service time

System utilization equation

System utilization= Customer arrival rate/ the number of servers (channels) X Service rate per server

Average number of customers being served equation

Avg number of customers being served= Customer arrival rate/ service rate per server

Little's law

For a stable system the avg number of customers in line or in the system is equal to the avg customer arrival rate multiplied by the avg time in the line or system
The avg number of customer in the system = Customer arrival rate X the avg time customer sp

Single server, constant service time

If a system can reduce variablility it can shorten waiting lines noticeably, for example by making service time constant, the avg number of customers waiting in line can be cut in half
Avg time customers spend waiting in line is also cut in half
Similiar

Multiple servers assumptions

A poisson arrival rate and exponential service time
Servers all work at the same avg rate
Customers form a single waiting line

Cost Analysis

Service system design reflects the desire of mgt to balance the cost of capacity with the expected cost of customers waiting in the system
Optimal capacity is one that minimizes the sum of waiting costs and capacity or server costs

Multiple prioity model

Customers are processed according to some measure of importance. Customers are assigned to one serveral priority classes according to some predetermined assignment method
Customers are then processed by class, highest class first
Within a class customers

Finite source model

Appropriate for cases in which the calling population is limited to a relatively small number of potential calls
Arrival rates are required to be Poisson
Unlike the infinite source models, the arrival rate is affected by the length of the waiting line
The

Finite Source model procedure

Identify the values for
N, pop size
M, number of servers/ channels
T, average service time
U, average time between calls for service
Compute service factor, X= T/ (T+U)
Locate section of the finite queing tables for N
Using the value of X as the point of

Constraing management

Managers may be able to reduce waiting lines by actively managing one or more system constrains:
Fixed short term constraints:
facility size, number of servers
Short term capacity options
use temporary workers, shift demand, standardize the service, look

Psych of waiting

If those waiting in line have nothing else to occupy their thoughts they often tend to focus that they are waiting in line and will percieve the waiting time to be longer than it actually is
Steps to make waiting more acceptable:
Occupy them while they wa

Options for reducing waiting lines

Work to increase processing rates instead of increasing servers
Use new processing equip
Reduce processing time through standardization
shift demand