Consider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served\nbasis. Suppose the probability density function f(t) and the cumulative distribution function f(t) of the interarrival time are such\nthat the rate f(t)/ [1 ? F(T)] tends to a constant asT ? ?, and the rate computed fromthe distribution of the service time tends to\nanother constant.When the queue is in a stationary state, we derive a set of equations for the probabilities of the queue length and\nthe states of the arrival and service processes. Solving the equations, we obtain approximate results for the stationary probabilities\nwhich can be used to obtain the stationary queue length distribution and waiting time distribution of a customer who arrives when\nthe queue is in the stationary state.
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