This study was concerned with some aspects of single server queues where customers arrive singly to receive some kind of service from a server. We discussed in detail the queueing models for different specifications of arrival and service pattern. The emphasis was given on distribution of queue size, waiting time, sojourn time and busy period.A particular queueing model has also been considered in chapter four. In production process, sometimes it is costly to keep the machine on when there are no jobs to be processed. It has been suggested that it could be reasonable to set up a threshold number of jobs after which the machine may be switched on. We also collected primary data from the out door unit of Urology department of Bangabandhu Sheikh Mujib Medical University Hospital to get an idea about the queueing pattern formed there and found that the arrival pattern of patients followed Poisson distribution, interarrival time followed exponential distribution and the service time distribution was also exponential. Some important characteristics of queue such as traffic intensity, expected value of queue length, waiting time, sojourn time, busy period etc. were also computed.

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