Related papers: Queue-length balance equations in multiclass multi…
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 $\Delta$…
Motivated by applications that involve setting proper staffing levels for multi-server queueing systems with batch arrivals, we present a thorough study of the queue-length process $\{Q(t); t \geq 0\}$, departure process $\{D(t); t \geq…
We consider a polling system: a queueing system of $N\ge 1$ queues with Poisson arrivals $Q_1,...,Q_N$ visited in a cyclic order (with or without switchover times) by a single server. For this system we derive the probability generating…
In many different settings, requests for service can arrive in near or true simultaneity with one another. This creates batches of arrivals to the underlying queueing system. In this paper, we study the staffing problem for the batch…
This paper addresses the analysis of the queue-length process of single-server queues under overdispersion, i.e., queues fed by an arrival process for which the variance of the number of arrivals in a given time window exceeds the…
A simple analytical solution is proposed for the stationary loss system of two parallel queues with finite capacity $K$, in which new customers join the shortest queue, or one of the two with equal probability if their lengths are equal.…
Gaitonde and Tardos recently studied a model of queueing networks where queues compete for servers and re-send returned packets in future rounds. They quantify the amount of additional processing power that guarantees a decentralized…
Let $X$ be the constrained random walk on ${\mathbb Z}_+^2$ with increments $(1,0)$, $(-1,0)$, $(0,1)$ and $(0,-1)$; $X$ represents, at arrivals and service completions, the lengths of two queues working in parallel whose service and…
Stability with respect to a given scheduling policy has become an important issue for wireless communication systems, but it is hard to prove in particular scenarios. In this paper two simple conditions for stability in broadcast channels…
Information-theoretic arguments focus on modeling the reliability of information transmission, assuming availability of infinite data at sources, thus ignoring randomness in message generation times at the respective sources. However, in…
We introduce a rate balance principle for general (not necessarily Markovian) stochastic processes. Special attention is given to processes with birth and death like transitions, for which it is shown that for any state $i$, the rate of two…
This paper considers a multiclass processor-sharing queue with feedback. Jobs arrive according to renewal processes, and service times follow general distributions. Upon service completion, jobs may either depart the system or re-enter as a…
We consider a system of N queues with decentralized load balancing such as power-of-D strategies(where D may depend on N) and generic scheduling disciplines. To measure the dependence of the queues, we use the clan of ancestors, a technique…
The Load-Balanced Router architecture has received a lot of attention because it does not require centralized scheduling at the internal switch fabrics. In this paper we reexamine the architecture, motivated by its potential to turn off…
We analyze a tandem network of polling queues with two product types and two stations. We assume that external arrivals to the network follow a Poisson process, and service times at each station are exponentially distributed. For this…
This paper presents a method for calculating steady state probabilities of $M|E_r|c|K$ queueing systems. The infinitesimal generator matrix is used to define all possible states in the system and their transition probabilities. While this…
This paper considers a BMAP/M/$\infty$ queue with a batch Markovian arrival process (BMAP) and an exponential service time distribution. We first prove that the BMAP/M/$\infty$ queue is stable if and only if the expectation of the logarithm…
Recent years have seen a great increase in the capacity and parallel processing power of data centers and cloud services. To fully utilize the said distributed systems, optimal load balancing for parallel queuing architectures must be…
We consider a tandem queue with coupled processors, which is subject to global breakdowns. When the network is in the operating mode and both queues are non empty, the total service capacity is shared among the stations according to fixed…
We consider a one-dimensional stochastic reaction-diffusion generalizing the totally asymmetric simple exclusion process, and aiming at describing single lane roads with vehicles that can change speed. To each particle is associated a jump…