Related papers: Exact asymptotics in an infinite-server system wit…
Many networking-related settings can be modeled by Markov-modulated infinite-server systems. In such models, the customers' arrival rates and service rates are modulated by a Markovian background process, additionally, there are infinitely…
In this paper, we consider a discrete-time preemptive priority queue with different service rates for two classes of customers, one with high-priority and the other with low-priority. This model corresponds to the classical preemptive…
We obtain asymptotic bounds for the tail distribution of steady-state waiting time in a two server queue where each server processes incoming jobs at a rate equal to the rate of their arrivals (that is, the half-loaded regime). The job…
We study the asymptotics of the stationary sojourn time Z of a "typical customer" in a tandem of single-server queues. It is shown that, in a certain "intermediate" region of light-tailed service time distributions, Z may take a large value…
We consider a single-server GI/GI/1 queueing system with feedback. We assume the service times distribution to be (intermediate) regularly varying. We find the tail asymptotics for a customer's sojourn time in two regimes: the customer…
The model is motivated by the problem of load distribution in large-scale cloud-based data processing systems. We consider a heterogeneous service system, consisting of multiple large server pools. The pools are different in that their…
This paper studies the effect of an overdispersed arrival process on the performance of an infinite-server system. In our setup, a random environment is modeled by drawing an arrival rate $\Lambda$ from a given distribution every $\Delta$…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
We revisit a single-server retrial queue with two independent Poisson streams (corresponding to two types of customers) and two orbits. The size of each orbit is infinite. The exponential server (with a rate independent of the type of…
This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…
We are interested in a large queue in a $GI/G/k$ queue with heterogeneous servers. For this, we consider tail asymptotics and weak limit approximations for the stationary distribution of its queue length process in continuous time under a…
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…
This paper addresses the problem of outage characterization of an ambient backscatter communication system with a pair of passive tag and reader. In particular, an exact expression for the effective channel distribution is derived. Then,…
In the context of communication networks, the framework of stochastic event graphs allows a modeling of control mechanisms induced by the communication protocol and an analysis of its performances. We concentrate on the logarithmic tail…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
We consider sojourn (or response) times in processor-shared queues that have a finite customer capacity. Computing the response time of a tagged customer involves solving a finite system of linear ODEs. Writing the system in matrix form, we…
Stochastic networks with complex structures are key modelling tools for many important applications. In this paper, we consider a specific type of network: the retrial queueing systems with priority. This type of queueing system is…
The goal of the paper is to study asymptotic behavior of the number of lost messages. Long messages are assumed to be divided into a random number of packets which are transmitted independently of one another. An error in transmission of a…
A large-scale service system with multiple customer classes and multiple server pools is considered, with the mean service time depending both on the customer class and server pool. The allowed activities (routing choices) form a tree (in…
In this note we essentially simplify the proof of the main result in one paper from leading computer science conference 25th ACM Symposium on Parallelism in Algorithms and Architectures (see [3].) We also present direct method and give…