Queuing Theory
TOPIC VII
QUEUING THEORY
Definition
A queue can be defined as items awaiting service. Queues may consist of people, cars, components awaiting machining, telephone calls, aeroplanes, indeed any discrete items.
Queues form when the rate of arrival of items requiring service is greater than the rate of service.
Queuing theory can be defined as the construction of mathematical models of various types of queuing systems so that predictions may be made about how the system works with the demands made upon it.
Applications
Queuing theory may be applied in the following areas: a) Shop counters. Customers arrive at varying intervals requiring service which takes a variable time. What is number of assistants that will maximize profit, or provide the best service? b) Telephone exchange. The smaller the exchange the lower the cost but the greater the congestion. The larger the exchange the higher the costs but with reduced congestion. c) Parts stores. Production workers waiting to draw out parts. What is the appropriate number of service points and staff to produce lowest overall cost? d) Airport runways. How many runways are needed to provide landing facilities after a reasonable queue time?
Terms used in Queuing Theory
Customer- persons or units arriving at a station or service
Service station- point where service is provided
Waiting time- time a customer spends in the queue before being served
Time spent by a customer in the system- waiting time plus service time
Number of customers in the system- number of customers in the queue plus those being served
Queue length- number of customers waiting in the queue
Jockeying- joining the other queue and leaving the first one
Reneging- joining the queue and leaving it afterwards
Balking- customer decides not to join the queue
Queuing system- system consisting arrival of customers, waiting in queue, picked up for service according to a certain discipline, before
QUEUING THEORY
Definition
A queue can be defined as items awaiting service. Queues may consist of people, cars, components awaiting machining, telephone calls, aeroplanes, indeed any discrete items.
Queues form when the rate of arrival of items requiring service is greater than the rate of service.
Queuing theory can be defined as the construction of mathematical models of various types of queuing systems so that predictions may be made about how the system works with the demands made upon it.
Applications
Queuing theory may be applied in the following areas: a) Shop counters. Customers arrive at varying intervals requiring service which takes a variable time. What is number of assistants that will maximize profit, or provide the best service? b) Telephone exchange. The smaller the exchange the lower the cost but the greater the congestion. The larger the exchange the higher the costs but with reduced congestion. c) Parts stores. Production workers waiting to draw out parts. What is the appropriate number of service points and staff to produce lowest overall cost? d) Airport runways. How many runways are needed to provide landing facilities after a reasonable queue time?
Terms used in Queuing Theory
Customer- persons or units arriving at a station or service
Service station- point where service is provided
Waiting time- time a customer spends in the queue before being served
Time spent by a customer in the system- waiting time plus service time
Number of customers in the system- number of customers in the queue plus those being served
Queue length- number of customers waiting in the queue
Jockeying- joining the other queue and leaving the first one
Reneging- joining the queue and leaving it afterwards
Balking- customer decides not to join the queue
Queuing system- system consisting arrival of customers, waiting in queue, picked up for service according to a certain discipline, before