Related papers: First exit time for a discrete time parallel queue
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
We study a queueing system with Erlang arrivals with $k$ phases and Erlang service with $m$ phases. Transition rates among phases vary periodically with time. For these systems, we derive the asymptotic periodic distribution of the level…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
We consider the problem of simultaneous scheduling and resource allocation of an incoming flow of requests to a set of computing units. By representing each computing unit as a node, we model the overall system as a multi-queue scheme.…
In this work, we study the impact of a relay node to a network with a finite number of users-sources and a destination node. We assume that the users have saturated queues and the relay node does not have packets of its own; we have random…
Queuing models provide insight into the temporal inhomogeneity of human dynamics, characterized by the broad distribution of waiting times of individuals performing tasks. We study the queuing model of an agent trying to execute a task of…
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…
We consider random-access networks where nodes represent servers with a queue and can be either active or inactive. A node deactivates at unit rate, while it activates at a rate that depends on its queue length, provided none of its…
We consider a system of ordered cars moving in $\R$ from right to left. Each car is represented by a point in $\R$; two or more cars can occupy the same point but cannot overpass. Cars have two possible velocities: either 0 or 1. An…
In this paper, we discuss an interesting but challenging bilateral stochastically matching problem: A more general matched queue with matching batch pair (m, n) and two types (i.e., types A and B) of impatient customers, where the arrivals…
We consider a two-queue polling model with switch-over times and $k$-limited service (serve at most $k_i$ customers during one visit period to queue $i$) in each queue. The major benefit of the $k$-limited service discipline is that it -…
Maximizing throughput for heterogeneous parallel server queues has received quite a bit of attention from the research community and the stability region for such systems is well understood. However, many real-world systems have periods…
We introduce the first class of perfect sampling algorithms for the steady-state distribution of multi-server queues with general interarrival time and service time distributions. Our algorithm is built on the classical dominated coupling…
We consider multiclass feedforward queueing networks with first in first out and priority service disciplines at the nodes, and class dependent deterministic routing between nodes. The random behavior of the network is constructed from…
We consider a single server retrial queue with the server subject to interruptions and classical retrial policy for the access from the orbit to the server. We analyze the equilibrium distribution of the system and obtain the generating…
We consider a service system with an infinite number of exponential servers sharing a finite service capacity. The servers are ordered according to their speed, and arriving customers join the fastest idle server. A capacity allocation is…
We use fluid limits to explore the (in)stability properties of wireless networks with queue-based random-access algorithms. Queue-based random-access schemes are simple and inherently distributed in nature, yet provide the capability to…
We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast,…
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…
We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…