The probability distribution of the number of customers accumulated when a vacation ends in the Geo/G/1 gated system

We present a procedure which finds the probability distribution of number of customers accumulated when the server ends a vacation in the Geo/G/1 gated queueing system, where the service for a customer and the vacation, respectively, takes one slot time. The p.g.f. for the number of customers accumulated at the gate closing epoch is obtained as a recursive form. The full probabilities, then, are derived using an iterative procedure. This system finds an application in a packet transmitting telecommunications system where the server transmits (serves) packets (customers) accumulated at a gate closing epoch, and takes one slot time vacation thereafter.