In designing a good queuing system, it is necessary to have good information about the model. The characteristics listed below would provide sufficient information.
The Arrival Pattern
The simplest arrival process is one where we have completely regular arrivals (i.e. the same constant time interval between successive arrivals). A Poisson stream of arrivals corresponds to arrivals at random. In a Poisson stream successive customers arrive after intervals which independently are exponentially distributed.
The Poisson stream is important as it is a convenient mathematical model of many real life queuing systems and is described by a single parameter - the average arrival rate. Other important arrival processes are scheduled arrivals; batch arrivals; and time dependent arrival rates (i.e. the arrival rate varies according to the time of day).
The essential features of queing management system in operations research are
The Service Mechanism
Assuming that the service times for customers are independent and do not depend upon the arrival process is common. Another common assumption about service times is that they are exponentially distributed.
The Queue Discipline
In the queue structure, the important thing to know is the queue discipline. The queue discipline is the order or manner in which customers from the queue are selected for service.
There are a number of ways in which customers in the queue are served. Some of these are:
(a) Static queue disciplines are based on the individual customer's status in the queue. Few of such disciplines are:
(b) Dynamic queue disciplines are based on the individual customer attributes in the queue. Few of such disciplines are:
For the queuing models that we shall consider, the assumption would be that the customers are serviced on the first-come-first-served basis.
The Number of Customers allowed in the System
In certain cases, a service system is unable to accommodate more than the required number of customers at a time. No further customers are allowed to enter until space becomes available to accommodate new customers. Such type of situations are referred to as finite (or limited) source queue. Examples of finite source queues are cinema halls, restaurants, etc.
On the other hand, if a service system is able to accommodate any number of customers at a time, then it is referred to as infinite (or unlimited) source queue. For example, in a sales department, here the customer orders are received; there is no restriction on the number of orders that can come in, so that a queue of any size can form.
The Number of Service Channels
The more the number of service channels in the service facility, the greater the overall service rate of the facility. The combination of arrival rate and service rate is critical for determining the number of service channels. When there are a number of service channels available for service, then the arrangement of service depends upon the design of the system's service mechanism.
Parallel channels means, a number of channels providing identical service facilities so that several customers may be served simultaneously. Series channel means a customer go through successive ordered channels before service is completed. A queuing system is called a one-server model, i.e., when the system has only one server, and a multi-server model i.e., when the system has a number of parallel channels, each with one server.
(a) Arrangement of service facilities in series
(1) Single Queue Single Server
(2) Single Queue, Multiple Server
(b) Arrangement of Service facilities in Parallel
(c) Arrangement of Mixed Service facilities
Arrangements of Service Facilities (a, b, c)
Attitude of Customers
Patient Customer: Customer arrives at the service system, stays in the queue until served, no matter how much he has to wait for service.
Impatient Customer: Customer arrives at the service system, waits for a certain time in the queue and leaves the system without getting service due to some reasons like long queue before him.
Balking: Customer decides not to join the queue by seeing the number of customers already in service system.
Reneging: Customer after joining the queue, waits for some time and leaves the service system due to delay in service.
Jockeying: Customer moves from one queue to another thinking that he will get served faster by doing so.
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