198 research outputs found
Analysis and optimization of vacation and polling models with retrials
We study a vacation-type queueing model, and a single-server multi-queue
polling model, with the special feature of retrials. Just before the server
arrives at a station there is some deterministic glue period. Customers (both
new arrivals and retrials) arriving at the station during this glue period will
be served during the visit of the server. Customers arriving in any other
period leave immediately and will retry after an exponentially distributed
time. Our main focus is on queue length analysis, both at embedded time points
(beginnings of glue periods, visit periods and switch- or vacation periods) and
at arbitrary time points.Comment: Keywords: vacation queue, polling model, retrials Submitted for
review to Performance evaluation journal, as an extended version of 'Vacation
and polling models with retrials', by Onno Boxma and Jacques Resin
Workloads and waiting times in single-server systems with multiple customer classes
One of the most fundamental properties that single-server multi-class service systems may possess is the property of work conservation. Under certain restrictions, the work conservation property gives rise to a conservation law for mean waiting times, i.e., a linear relation between the mean waiting times of the various classes of customers. This paper is devoted to single-server multi-class service systems in which work conservation is violated in the sense that the server's activities may be interrupted although work is still present. For a large class of such systems with interruptions, a decomposition of the amount of work into two independent components is obtained; one of these components is the amount of work in the corresponding systemwithout interruptions. The work decomposition gives rise to a (pseudo)conservation law for mean waiting times, just as work conservation did for the system without interruptions
Queueing system with vacations after a random amount of work
This paper considers an M/G/1 queue with the following vacation discipline. The server takes a vacation as soon as it has served a certain amount of work since the end of the previous vacation. If the system becomes empty before the server has completed this amount of work, then it stays idle until the next customer arrival and then becomes active again. Such a vacation discipline arises, for example, in the maintenance of production systems, where machines or equipment mainly degrade while being operational. We derive an explicit expression for the distribution of the time it takes until the prespecified amount of work has been served. For the case the total amount of work till vacation is exponentially distributed, we derive the transforms of the steady-state workload at various epochs, busy period, waiting time, sojourn time, and queue length distributions
Wait-and-see strategies in polling models
We consider a general polling model with stations. The stations are
served exhaustively and in cyclic order. Once a station queue falls empty, the
server does not immediately switch to the next station. Rather, it waits at the
station for the possible arrival of new work ("wait-and-see") and, in the case
of this happening, it restarts service in an exhaustive fashion. The total time
the server waits idly is set to be a fixed, deterministic parameter for each
station. Switchover times and service times are allowed to follow some general
distribution, respectively. In some cases, which can be characterised, this
strategy yields strictly lower average queueing delay than for the exhaustive
strategy, which corresponds to setting the "wait-and-see credit" equal to zero
for all stations. This extends results of Pek\"oz (Probability in the
Engineering and Informational Sciences 13 (1999)) and of Boxma et al. (Annals
of Operations Research 112 (2002)). Furthermore, we give a lower bound for the
delay for {\it all} strategies that allow the server to wait at the stations
even though no work is present.Comment: 24p, submitte
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