Performance analysis of polling systems with retrials and glue periods

摘要

We consider gated polling systems with two special features: (i) retrials,and (ii) glue or reservation periods. When a type-$i$ customer arrives, orretries, during a glue period of station $i$, it will be served in the nextvisit period of the server to that station. Customers arriving at station $i$in any other period join the orbit of that station and retry after anexponentially distributed time. Such polling systems can be used to study theperformance of certain switches in optical communication systems. For the case of exponentially distributed glue periods, we present analgorithm to obtain the moments of the number of customers in each station. Forgenerally distributed glue periods, we consider the distribution of the totalworkload in the system, using it to derive a pseudo conservation law which inits turn is used to obtain accurate approximations of the individual meanwaiting times. We also consider the problem of choosing the lengths of the glueperiods, under a constraint on the total glue period per cycle, so as tominimize a weighted sum of the mean waiting times.