Performance analysis of polling systems with retrials and glue periods

We consider gated polling systems with two special features: (i) retrials, and (ii) glue or reservation periods. When a type-$i$ customer arrives, or retries, during a glue period of station $i$, it will be served in the next visit 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 an exponentially distributed time. Such polling systems can be used to study the performance of certain switches in optical communication systems. For the case of exponentially distributed glue periods, we present an algorithm to obtain the moments of the number of customers in each station. For generally distributed glue periods, we consider the distribution of the total workload in the system, using it to derive a pseudo conservation law which in its turn is used to obtain accurate approximations of the individual mean waiting times. We also consider the problem of choosing the lengths of the glue periods, under a constraint on the total glue period per cycle, so as to minimize a weighted sum of the mean waiting times

Approximations for multiserver queues with balking/retrial discipline

Queueing models including the effects of repeated attempts have wide practical use in designing communication systems. The model studied in this paper not only takes into account retrials due to congestion but also considers the effects of balking discipline. Two approximations are considered in order to study the system behaviour for low retrial intensity

Retrial queueing model with two-way communication, unreliable server and resume of interrupted call for cognitive radio networks

In this paper, we consider a single server queueing model M/GI/GI/1/1 with two types of calls: incoming calls and outgoing calls. Incoming call enters the system and goes into service if the server is free. If the server is busy, call instantly goes to orbit, after which the call retries to go into service. The server makes an outgoing call in its idle time. We will be reviewing a system with unreliable server. In a free state and while servicing outgoing calls the server is reliable and unable to crash. If while servicing incoming call the server crashes, the incoming call stays at the server and as soon as server recovers the call goes into afterservice. For that system we’ve obtained probability distribution of server states, condition for the existence of a stationary mode and probability distribution of a number of incoming calls in the system