51 research outputs found
A sufficient condition for the subexponential asymptotics of GI/G/1-type Markov chains with queueing applications
The main contribution of this paper is to present a new sufficient condition
for the subexponential asymptotics of the stationary distribution of a
GI/GI/1-type Markov chain without jumps from level "infinity" to level zero.
For simplicity, we call such Markov chains {\it GI/GI/1-type Markov chains
without disasters} because they are often used to analyze semi-Markovian queues
without "disasters", which are negative customers who remove all the customers
in the system (including themselves) on their arrivals. In this paper, we
demonstrate the application of our main result to the stationary queue length
distribution in the standard BMAP/GI/1 queue. Thus we obtain new asymptotic
formulas and prove the existing formulas under weaker conditions than those in
the literature. In addition, applying our main result to a single-server queue
with Markovian arrivals and the -bulk-service rule (i.e., MAP//1 queue), we obatin a subexponential asymptotic formula for the
stationary queue length distribution.Comment: Submitted for revie
Tail asymptotics for cumulative processes sampled at heavy-tailed random times with applications to queueing models in Markovian environments
This paper considers the tail asymptotics for a cumulative process sampled at a heavy-tailed random time . The main contribution of
this paper is to establish several sufficient conditions for the asymptotic
equality as , where and is a certain
positive constant. The main results of this paper can be used to obtain the
subexponential asymptotics for various queueing models in Markovian
environments. As an example, using the main results, we derive subexponential
asymptotic formulas for the loss probability of a single-server finite-buffer
queue with an on/off arrival process in a Markovian environment
Two queues with random time-limited polling
In this paper, we analyse a single server polling model with two queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server that serves both queues with generally distributed service times. The server spends an exponentially distributed amount of time in each queue. After the completion of this residing time, the server instantaneously switches to the other queue, i.e., there is no switch-over time. For this polling model we derive the steady-state marginal workload distribution, as well as heavy traffic and heavy tail asymptotic results. Furthermore, we also calculate the joint queue length distribution for the special case of exponentially distributed service times using singular perturbation analysis
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