arXiv subjects

Rudesindo Núñez Queija

Publications and source records attributed to Rudesindo Núñez Queija.

3 recordsLinked to original sources

arXiv2018

Heavy-traffic analysis of the $M^X/\text{semi-Markov}/1$ queue

In this paper we analyze a single server queue with batch arrivals and semi-Markovian service times. We also include the feature that the first service of each busy period might have a different distribution than subsequent service times. Our generating function based approach allows us to determine the heavy traffic limit of the scaled queue-length distribution. It turns out that this distribution converges to an exponential distribution. Nonsurprisingly, the exceptional first service does not influence this limiting distribution. We identify a sufficient and necessary condition under which the dependence between successive service times disappears in the limit, which we illustrate in a numerical example.

math.PR↗

arXiv2017

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.

math.PR↗

arXiv2012

Waiting time asymptotics in the single server queue with service in random order

We consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals and regularly varying service time distribution with index -ν, it is shown that the waiting time distribution is also regularly varying, with index 1 -ν, and the pre-factor is determined explicitly. Another contribution of the paper is the heavy-traffic analysis of the waiting time distribution in the M/G/1 case. We consider not only the case of finite service time variance, but also the case of regularly varying service time distribution with infinite variance.

math.PR↗