When a Queue Looks the Same to an Arriving Customer as to an Observer

Ralph E. Strauch

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Advanced Queuing Theory Analysis Probability and Statistical Research Optimization and Search Problems

Abstract

In a queue with a Poisson arrival distribution, the probability distribution state of the queue at any time is independent of whether or not an arrival occurs at that time. In particular, in a stationary queue with Poisson arrivals, the stationary distribution of the number of waiting customers in the queue at an arbitrary time is equal to the stationary distribution of the number of customers waiting in the queue when a new customer arrives.

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1971On One-For-One-Ordering Inventory Policies with State-Dependent Leadtimes 1978Analysis and Applications of the Delay Cycle for the M/M/c Queueing System 2018A fuzzy inventory model with acceptable shortage using graded mean integration value method 1984Inequalities between Arrival Averages and Time Averages in Stochastic Processes Arising from Queueing Theory 1983Stationary queuing systems with dependencies

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