Abstract
This work analysis some discrete-time queueing mechanisms with infinitely many servers.By using a shot noise process, general results on the system size in discrete-time are given both in transient state and in steady state. For this we use the classical differentiation formula of F´a di Bruno. First two moments of the system size and distribution of the busy period of the system are also computed.
Highlights
This work analysis some discrete-time queueing mechanisms with infinitely many servers
The number of busy servers or the number of customers in the system in transient state can be modelled as a shot noise process which is the superposition of shot effects caused by the arrivals at random epochs
In discrete-time queueing systems, time is considered as a discrete random variable and the events occur only at definite time points called “time marks” by Meisling
Summary
This work analysis some discrete-time queueing mechanisms with infinitely many servers. The number of busy servers or the number of customers in the system in transient state can be modelled as a shot noise process which is the superposition of shot effects caused by the arrivals at random epochs. Arrivals occur only at these time marks which are assumed to be regularly spaced and service is initiated The mean number of busy servers and its variance at arbitrary epochs are found.
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