The word â€˜queueâ€™ is not unfamiliar to us. We have all stood in a queue for railways reservations, or airline tickets, in a ration shop, or for water from a municipal tanker. System 1 shows a simple system where there is one servicing person or servicing point and one line of customers waiting to be service to be performed on them. A Customer will go through all these multiple services. The third system shows a number of servers performing the same type of service who are service providers. The third system shows a number of servers performing the same type of service who are available for the customers waiting in line. As soon as any one of the servers become available, the customer waiting in the line can go to that particular free server to get the desired service. The fourth category of the queuing system has a number of different kinds of services to be performed one after another where a number of servers are available to perform the same kind of service. This is the generalized version of the queuing system. Queuing theory models are different for these different categories of queuing systems.
The questions to be asked in queuing theory analysis are, for example:
1. What is the average number of units (i.e. customers, jobs) waiting in the queue?
2. What is the average waiting time for the units in the queue system? What is the waiting time for the different types of units if such a differentiation exists and is necessary?
3. What are the criteria of performance for the queue system?
4. How might one design/change the service and/or arrival characteristics of the system?
5. How might one, suitably, design the Queuing Discipline to achieve the desired objective/s?
6. In the achievement of one objective, how can the other objective/s possibly be compromised?
The analysis of the Queuing systems should provide us with a number of scenarios for policy alternatives with the corresponding expected results. Queuing theory is a decision making tool for the managerâ€™s benefit, just as the other Operations Research techniques. In other words, waiting line length may be designed to be longer or shorter, depending on the class of â€œcustomersâ€, or the waiting line length and waiting time may not be of primary significance, all depending upon the objectives and criteria for the system.
Characteristics of Single Channel single service Queuing System:
This is one of the basic analytical queuing models. The assumptions are:
1. Single channel single service.
2. The distribution of arrival rates is modeled by Poisson distribution.
3. The distribution of service rates is also modeled by Poisson distribution.
4. The Queue Discipline is first come first served (FCFS).
5. It is possible for the waiting line to grow infinitely long
6. The queue system does not influence either the arrival or services rates.
7. Each arrival (customer) needs the same unit of service.
Arrival from a Finite Population:
While the case of the applicants can be from an infinite (almost) source, the cases of (i) machines breaking down and arriving for service (ii) second year MBA repeater students coming to a teacher for doubts, are not arrivals drawn from an infinite source. The source is finite and hence the arrival process characteristics get affected by the number in the queuing system. Generally, with a number in the source above 30, the assumption of infinite source holds quite well. However, with a finite source, the formulae are different and are cumbersome for manual computations. Finite Queuing Tables will help in such cases.