We consider the FCFS GI/GI/n queue in the Halfin-Whitt heavy traffic regime, in the presence of heavy-tailed distributions (i.e. infinite variance). We prove that under minimal assumptions, i.e. only that processing times have finite 1 + moment for some > 0 and inter-arrival times have finite second moment, the sequence of stationary queue length distributions, normalized by n 1 2 , is tight in...

We present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. Under typical heavy traffic assumptions, we prove a diffusion limit theorem for a measure-valued state descriptor, from which we conclude a similar theorem for the queue length proces...

The problem considered is that of estimating the tail stationary probability for two exponential server queues in series fed by renewal arrivals. We compute the tail of the marginal queue length distribution at the second queue. The marginal at the first queue is known by the classical result for the GI/M/1 queue. The approach involves deriving necessary and sufficient conditions on the paths o...

The data transmission in wireless networks is usually analyzed under the assumption of non-stationary rates. Nevertheless, they strictly depend on time day, that is, intensity arrival and daily workload profiles confirm this fact. In article, we consider process downloading a file within single network segment unsteady speeds—for arrivals, sizes, losses due to impatience. To simulate scenario, ...

We study the steady-state queue-length vector in a multi-class queue with relative priorities. Upon service completion, the probability that the next served customer is from class k is controlled by class-dependent weights. Once a customer has started service, it is served without interruption until completion. We establish a state-space collapse for the scaled queue length vector in the heavy-...

We study the impact of service time distributions on the distribution ofthe maximum queue length during a busy period for the Mx/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer size for finite-buffer (M/G/1/n) systems. We show the somewhat surprising result that, for three variations of the preemptive last-come-first-served discipline,...

In this paper ,we discuss the Geom/G/1 queue with Bernoulli feedback and server setup/closedown times.We derive the probability generating function (PGF) of the steady-state queue length immediately after a service completion by the embedded Markov chain and the PGF of the queue length immediately after an arbitrary slot boundary .We also get the PGF of the stationary waiting times under first ...

Information about queue length is an important parameter for customers who face the decision whether to join a queue or not. In this paper, we study how optimal information disclosure policies can be used by a service provider of an M/M/1 queue to increase its revenue. Our main contribution is showing that the intuitive policy of informing customers about the current queue length when it is sho...

This paper deals with the study of multi-server queueing model in a fuzzy environment imposition reneging customers. Entry customers system is assumed to be Poisson process and exponential service time distribution under first-come-first-served basis. Specific this investigation derive various performance measures such as queue length, waiting queue, response optimal number servers explicit for...