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Abstract

The Pollaczek-Khinchin transform equation is usually derived by means of the embedded Markov chain technique considering the number of customers in an M/G/1 queueing system at moments just after having served customers. The probabilities contained in this generating function, in [6] we determined them by using results from the theory of regenerative processes. The approach was based on the determination of mean values of times spent in different states in a busy period. Using the same general idea, we get an analogous result in the case of discrete time, for the Geo/G/1 system and derive the discrete-time version of the Pollaczek-Khinchin transform equation.

Keywords

Pollaczek-Khinchin transform equation Discrete queueing system Geo/G/1 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Eötvös Loránd UniversityBudapestHungary

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