Second Moment of Queue Size with Stationary Arrival Processes and Arbitrary Queue Discipline

In this paper we consider a queuing system in which the service times of customers are independent and identically distributed random variables, the arrival process is stationary and has the property of orderliness, and the queue discipline is arbitrary. For this queuing system we obtain the steady state second moment of the queue size in terms of the stationary waiting time distribution of a similar queuing system in which the queue discipline is first-in-first-out.

Keywords:

Queuing Theory , Stochastic processes , Applied Probability , Moments of Queue Size , Stochastic Service Systems