Queuing systems under various arrival and service policies

Abstract

In this thesis, a humble attempt has been made to contribute to two fields of queuing literature viz reneging phenomena and statistical inference in queuing theory. In most of the discussions in queuing theory it is assumed that once a customer joins the queue, it stays on the system till it completes its service. This notion is far removed from reality. In queues experienced in our day to day life customers who join the queue, have a patience span of their own. The moment he runs out of this patience span, he leaves the system irrespective of whether he has completed receiving service or not. Such customers are called reneged customers and the phenomenon is called reneging. Some common examples of reneging behaviour are Inventory Systems with perishable goods e.g. fruits, hospital emergency rooms handling critical patients, call abandonment in call centres etc. In general, reneging customers in queuing systems with limited waiting time can be classified into two types based upon when they could possibly renege. In the first type are customers who may renege only while waiting in queue. If they have reached the service stations, they do not renege. In the second type are those who may renege not only while waiting in queue but also while receiving service i.e. renege while waiting in the system, a caller calling up a call centre is an example of the first type. A critically injured motor vehicle accident victim entering a hospital emergency room is an example of the second type. The patient could expire, in other words renege, either while waiting in queue or while he is being attended to by doctors i.e. while receiving service. We have discussed both these variants in our analysis. The study of reneging has two broad aims. First, it should be able to measure the present status of reneging behaviour in terms of measurable performance parameters like rate of loss, fraction of customers who renege, probability of reneging, distribution and mean of waiting time for those who ultimately acquire service. Based upon...