21 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
Heavy traffic analysis of a polling model with retrials and glue periods
We present a heavy traffic analysis of a single-server polling model, with
the special features of retrials and glue periods. The combination of these
features in a polling model typically occurs in certain optical networking
models, and in models where customers have a reservation period just before
their service period. 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. As this model defies a closed-form
expression for the queue length distributions, our main focus is on their
heavy-traffic asymptotics, both at embedded time points (beginnings of glue
periods, visit periods and switch periods) and at arbitrary time points. We
obtain closed-form expressions for the limiting scaled joint queue length
distribution in heavy traffic and use these to accurately approximate the mean
number of customers in the system under different loads.Comment: 23 pages, 2 figure
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- customer arrives, or
retries, during a glue period of station , it will be served in the next
visit period of the server to that station. Customers arriving at station
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
A survey of the machine interference problem
This paper surveys the research published on the machine interference problem since the 1985 review by Stecke & Aronson. After introducing the basic model, we discuss the literature along several dimensions. We then note how research has evolved since the 1985 review, including a trend towards the modelling of stochastic (rather than deterministic) systems and the corresponding use of more advanced queuing methods for analysis. We conclude with some suggestions for areas holding particular promise for future studies.Natural Sciences and Engineering Research Council (NSERC) Discovery Grant 238294-200