Related papers: Tail Asymptotics for the $M_1,M_2/G_1,G_2/1$ Retri…
Randomized load-balancing algorithms play an important role in improving performance in large-scale networks at relatively low computational cost. A common model of such a system is a network of $N$ parallel queues in which incoming jobs…
The present paper is concerned with the stationary workload of queues with heavy-tailed (regularly varying) characteristics. We adopt a transform perspective to illuminate a close connection between the tail asymptotics and heavy-traffic…
Data center networks need to provide low latency, especially at the tail, as demanded by many interactive applications. To improve tail latency, existing approaches require modifications to switch hardware and/or end-host operating systems,…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
We consider the problem of packet scheduling in single-hop queueing networks, and analyze the impact of heavy-tailed traffic on the performance of Max-Weight scheduling. As a performance metric we use the delay stability of traffic flows: a…
We compute the tail asymptotics of the product of a beta random variable and a generalized gamma random variable which are independent and have general parameters. A special case of these asymptotics were proved and used in a recent work of…
When the arrival processes are Poisson, queueing networks are well-understood in terms of the product-form structure of the number of jobs $N_i$ at the individual queues; much less is known about the waiting time $W$ across the whole…
In many applications, significant correlations between arrivals of load-generating events make the numerical evaluation of the load of a system a challenging problem. Here, we construct very accurate approximations of the workload…
In wireless networks relay nodes can be used to assist the users' transmissions to reach their destination. Work on relay cooperation, from a physical layer perspective, has up to now yielded well-known results. This paper takes a different…
In this paper, asymptotic properties of the loss probability are considered for an M/G/1/N queue with server vacations and exhaustive service discipline, denoted by an M/G/1/N -(V, E)-queue. Exact asymptotic rates of the loss probability…
We consider a dynamic system with multiple types of customers and servers. Each type of waiting customer or server joins a separate queue, forming a bipartite graph with customer-side queues and server-side queues. The platform can match…
The problem of increased queueing delays in the Internet motivates the study of currently implemented transport protocols and active queue management (AQM) policies. We study Compound TCP (default protocol in Windows) with Random Early…
The presented study elaborates a multi-server priority queueing model considering the pre-emptive repeat policy and phase-type distribution (PH) for retrial process. The incoming heterogeneous calls are categorized as handoff calls and new…
This paper studies a service system in which arriving customers are provided with information about the delay they will experience. Based on this information they decide to wait for service or to leave the system. Specifically, every…
The theory community has proposed several new heap variants in the recent past which have remained largely untested experimentally. We take the field back to the drawing board, with straightforward implementations of both classic and novel…
We consider a stochastic network with mobile users in a heavy-traffic regime. We derive the scaling limit of the multi-dimensional queue length process and prove a form of spatial state space collapse. The proof exploits a recent result by…
We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by shot noise. A shot-noise rate emerges as a natural model, if the arrival rate tends…
It is well known that the probability distribution of high-frequency financial returns is characterized by a leptokurtic, heavy-tailed shape. This behavior undermines the typical assumption of Gaussian log-returns behind the standard…
In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in non-Jackson networks. This simplifying double-limit model, however, lends…
We consider a queue to which only a finite pool of $n$ customers can arrive, at times depending on their service requirement. A customer with stochastic service requirement $S$ arrives to the queue after an exponentially distributed time…