A single server Poisson arrival constant service time system, with server utilization less than 1 , will always have a smaller queue length as compared to a single server Poisson arrival general service system with same server utilization.

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Quizplus · Accepted Answer

In a Poisson arrival constant service time system, the inter-arrival times and service times are exponentially distributed. This means that the system is memoryless, and the queue length at any given time is independent of the past history of the system. In a Poisson arrival general service system, the service times are not exponentially distributed, and the system is not memoryless. This means that the queue length at any given time can be affected by the past history of the system. As a result, the queue length in a Poisson arrival constant service time system is always smaller than the queue length in a Poisson arrival general service system with the same server utilization.

A Single Server Poisson Arrival Constant Service Time System, with Server