2015
Transient analysis of cycle times in polling systems
Publication
Publication
We consider cyclic polling model with gated or globally gated service, and study
the transient behavior of all cycle lengths. Our aim is to analyze the dependency
structure between the different cycles, as this is an intrinsic property making polling
models challenging to analyze. Moreover, the cycle structure is related to the output
of a polling model and the current analysis may be useful to study networks
of polling models. In addition, transient performance is of great interest in systems
where disruptions or breakdowns may occur, leading to excessive cycle lengths. The
time to recover from such events is a primary performance measure. For the analysis
we assume that the distribution of the first cycle (globally gated) or N residence
times (gated), where N is the number of queues, is known. The joint Laplace-Stieltjes
transform (LST) of all x subsequent cycles (globally gated) or all x > N subsequent
residence times (gated) are then expressed in terms of the LST of the first cycle. From
this joint LST, we derive first and second moments and correlation coefficients between
different cycles. Finally, a heavy-tailed first cycle length or the heavy-traffic regime
provides additional insights in the time-dependent behavior.
Additional Metadata | |
---|---|
, | |
North-Holland | |
Performance Evaluation | |
Organisation | Directie |
van der Mei, R. (2015). Transient analysis of cycle times in polling systems. Performance Evaluation. |