Related papers: On Large Delays in Multi-Server Queues with Heavy …
We consider an extension of the standard G/G/1 queue, described by the equation $W\stackrel{\mathcal{D}}{=}\max\{0, B-A+YW\}$, where $\mathbb{P}[Y=1]=p$ and $\mathbb{P}[Y=-1]=1-p$. For $p=1$ this model reduces to the classical Lindley…
In this paper, we consider a load balancing system under a general pull-based policy. In particular, each arrival is randomly dispatched to one of the servers whose queue lengths are below a threshold, if there are any; otherwise, this…
We consider the steady-state distribution of the sojourn time of a job entering an M/GI/1 queue with the foreground-background scheduling policy in heavy traffic. The growth rate of its mean, as well as the limiting distribution, are…
In this paper, we investigate overlap times in a two-dimensional infinite server tandem queue. Specifically, we analyze the amount of time that a pair of customers spend overlapping in any station of the two dimensional tandem network. We…
We consider the FCFS $M/H_2/n + M$ queue in the Halfin-Whitt heavy traffic regime. It is known that the normalized sequence of steady-state queue length distributions is tight and converges weakly to a limiting random variable W. However,…
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…
We develop accurate approximations of the delay distribution of the MArP/G/1 queue that cap- ture the exact tail behavior and provide bounded relative errors. Motivated by statistical analysis, we consider the service times as a mixture of…
We consider a GI/H/n queueing system. In this system, there are multiple servers in the queue. The inter-arrival time is general and independent, and the service time follows hyper-exponential distribution. Instead of stochastic…
We use a series of pre-registered, incentive-compatible online experiments to investigate how people evaluate and choose among different waiting time distributions. Our main findings are threefold. First, consistent with prior literature,…
We study the impact of service-time distributions on the distribution of the maximum queue length during a busy period for the M^X/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer…
Understanding the generalization properties of heavy-tailed stochastic optimization algorithms has attracted increasing attention over the past years. While illuminating interesting aspects of stochastic optimizers by using heavy-tailed…
We consider a fixed-point equation for a non-negative integer-valued random variable, that appears in branching processes with state-independent immigration. A similar equation appears in the analysis of a single-server queue with a…
In traditional priority queues, we assume that every customer upon arrival has a fixed, class-dependent priority, and that a customer may not commence service if a customer with a higher priority is present in the queue. However, in…
We consider the $N$-model queueing system with a waiting time dependent threshold on the diagonal: the service discipline is First--Come--First--Served, but type-1 jobs can only be served by server 2 if their waiting time exceeds a…
We study a G/GI/1 single-server queuing model with i.i.d.\ service times that are independent of a stationary process of inter-arrival times. We show that the distribution of the waiting time converges to a stationary law as time tends to…
Recent development of peer-to-peer (P2P) services (e.g. streaming, file sharing, and storage) systems introduces a new type of queue systems that receive little attention before, where both job and server arrive and depart randomly. Current…
We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to -infinity and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we…
In this paper we revisit the results of Loynes (1962) on stability of queues for ergodic arrivals and services, and show examples when the arrivals are bounded and ergodic, the service rate is constant, and under stability the limit…
This paper considers the stationary distribution of the age of information (AoI) in information update systems. We first derive a general formula for the stationary distribution of the AoI, which holds for a wide class of information update…
We study the problem of scheduling jobs in a queueing system, specifically an M/G/1 with light-tailed job sizes, to asymptotically optimize the response time tail. This means scheduling to make $\mathbf{P}[T > t]$, the chance a job's…