论文信息 - 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

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

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 Ink functions introduced previously.

G. Luchak | George Luchak

[1] G. Luchak. The Solution of the Single-Channel Queuing Equations Characterized by a Time-Dependent Poisson-Distributed Arrival Rate and a General Class of Holding Times , 1956 .

[2] G. Reuter,et al. Spectral theory for the differential equations of simple birth and death processes , 1954, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.