The Distribution of the Time Required to Reduce to Some Preassigned Level a Single-Channel Queue Characterized by a Time-Dependent Poisson-Distributed Arrival Rate and a General Class of Holding Times

George Luchak
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George Luchak: Canadian Defence Research Board, Suffield Experimental Station, Ralston, Alberta, Canada

Operations Research, 1957, vol. 5, issue 2, 205-209

Abstract: This paper provides the solution to the problem of the distribution of busy periods of the single-channel queue characterized by a time-dependent Poisson-distributed arrival rate and a general class of holding times. The notation is chosen in such a fashion that the main body of computations and mathematical analysis is identical with what was required in the solution of the general queuing equations considered in a previous paper which should be read first [4] . The solution of the problem for which the traffic intensity is constant and the holding time distribution is Pearson type III is derived in closed form in terms of the I n k functions introduced previously.

Date: 1957
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