Related papers: Heavy-traffic asymptotic formulas for the multicla…
We consider a multi-server queue in the Halfin-Whitt regime: as the number of servers $n$ grows without a bound, the utilization approaches 1 from below at the rate $\Theta(1/\sqrt{n})$. Assuming that the service time distribution is…
We study a sequence of single server queues with customer abandonment (GI/GI/1+GI) under heavy traffic. The patience time distributions vary with the sequence, which allows for a wider scope of applications. It is known ([20, 18]) that the…
We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical…
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…
In this paper we study a two-queue polling model with zero switch-over times and $k$-limited service (serve at most $k_i$ customers during one visit period to queue $i$, $i=1,2$) in each queue. The arrival processes at the two queues are…
We obtain exact formulas for moments and generating functions of the height function of the asymmetric simple exclusion process at one spatial point, starting from special initial data in which every positive even site is initially…
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
Setting traffic light signals is a classical topic in traffic engineering, and important in heavy-traffic conditions when green times become scarce and longer queues are inevitably formed. For the fixed-cycle traffic-light queue, an…
In this paper, we analyze the steady state maximum overlap time in the M/M/1 queue. We derive the maximum overlap time tail distribution, its moments and the moment generating function. We also analyze the steady state minimum overlap time…
In the paper the flow in a thin tubular structure is considered. The velocity of the flow stands for a coefficient in the diffusion-convection equation set in the thin structure. An asymptotic expansion of solution is constructed. This…
This paper studies the input queued switch operating under the MaxWeight algorithm when the arrivals are according to a Markovian process. We exactly characterize the heavy-traffic scaled mean sum queue length in the heavy-traffic limit,…
We provide formulas for generating functions of many types of paths in various rooted tree structures. We compute the $k$th moment of the generating functions for various types of vertical paths. In two specific familes of trees we find…
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…
We consider the $\Delta_{(i)}/G/1$ queue, in which a a total of $n$ customers independently demand service after an exponential time. We focus on the case of heavy-tailed service times, and assume that the tail of the service time…
We introduce the notion of intensity reweighted moment pseudostationary point processes on linear networks. Based on arbitrary general regular linear network distances, we propose geometrically corrected versions of different higher-order…
The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the…
In the present paper a review and numerical comparison of a special class of multi-phase traffic theories based on microscopic, kinetic and macroscopic traffic models is given. Macroscopic traffic equations with multi-valued fundamental…
Stochastic driven flow along a channel can be modeled by the asymmetric simple exclusion process. We confirm numerically the presence of a dynamic queuing phase transition at a nonzero obstruction strength, and establish its scaling…
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we…
We derive asymptotic formulae for the coefficients of bivariate generating functions with algebraic and logarithmic factors. Logarithms appear when encoding cycles of combinatorial objects, and also implicitly when objects can be broken…