On the Geo/G/1 System
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  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.
KeywordsPollaczek-Khinchin transform equation Discrete queueing system Geo/G/1
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