CHARACTERISTICS OF QUEUING SYSTEM - Quantitative Techniques for management

In designing a good queuing system, it is necessary to have good information about the model. The characteristics listed below would provide sufficient information.

  1. The arrival pattern.
  2. The service mechanism.
  3. The queue discipline.
  4. The number of customers allowed in the system.
  5. The number of service channels.

The Arrival Pattern

  • How customers arrive e.g. singly or in groups (batch or bulk arrivals)
  • How the arrivals are distributed in time (e.g. what is the probability distribution of time between successive arrivals (the inter-arrival time distribution))
  • Whether there is a finite population of customers or (effectively) an infinite number

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).

Essential features of Queuing Management system in Operations Research

The essential features of queing management system in operations research are

The Service Mechanism

  • A description of the resources needed for service to begin
  • How long the service will take (the service time distribution)
  • The number of servers available
  • Whether the servers are in series (each server has a separate queue) or in parallel (one queue for all servers)
  • Whether preemption is allowed (a server can stop processing a customer to deal with another "emergency" customer)

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:

  1. If the customers are served in the order of their arrival, then this is known as the first-come, first-served (FCFS) service discipline. Prepaid taxi queue at airports where a taxi is engaged on a first-come, first-served basis is an example of this discipline.
  2. Last-come-first-served (LCFS)-- Sometimes, the customers are serviced in the reverse order of their entry so that the ones who join the last are served first. For example, assume that letters to be typed, or order forms to be processed accumulate in a pile, each new addition being put on the top of them. The typist or the clerk might process these letters or orders by taking each new task from the top of the pile. Thus, a just arriving task would be the next to be serviced provided that no fresh task arrives before it is picked up. Similarly, the people who join an elevator last are the first ones to leave it.

(b) Dynamic queue disciplines are based on the individual customer attributes in the queue. Few of such disciplines are:

  1. Service in Random Order (SIRO)-- Under this rule customers are selected for service at random, irrespective of their arrivals in the service system. In this every customer in the queue is equally likely to be selected. The time of arrival of the customers is, therefore, of no relevance in such a case.
  2. Priority Service-- Under this rule customers are grouped in priority classes on the basis of some attributes such as service time or urgency or according to some identifiable characteristic, and FCFS rule is used within each class to provide service. Treatment of VIPs in preference to other patients in a hospital is an example of priority service.

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

Arrangement of service facilities in series

(1) Single Queue Single Server

Single Queue Single Server

(2) Single Queue, Multiple Server

(b) Arrangement of Service facilities in Parallel

Arrangement of Service facilities in Parallel
(c) Arrangement of Mixed Service facilities

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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