Related papers: M/M/1 queue in two alternating environments and it…
We consider a class of discrete time Markov chains with state space [0,1] and the following dynamics. At each time step, first the direction of the next transition is chosen at random with probability depending on the current location. Then…
We consider a queueing system with $n$ parallel queues operating according to the so-called "supermarket model" in which arriving customers join the shortest of $d$ randomly selected queues. Assuming rate $n\lambda_{n}$ Poisson arrivals and…
Significant correlations between arrivals of load-generating events make the numerical evaluation of the workload of a system a challenging problem. In this paper, we construct highly accurate approximations of the workload distribution of…
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…
This paper proposes a stochastic framework to evaluate the performance of public transit systems under short random service suspensions. We aim to derive closed-form formulations of the mean and variance of the queue length and waiting…
The drift method was recently developed to study queueing systems in steady-state. It was successfully used to obtain bounds on the moments of the scaled queue lengths, that are asymptotically tight in heavy-traffic, in a wide variety of…
Motivated by applications arising in networked systems, this work examines controlled regime-switching systems that stem from a mean-variance formulation. A main point is that the switching process is a hidden Markov chain. An additional…
We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be non-zero number of buyers and sellers…
Motivated by queueing systems with heterogeneous parallel servers, we consider a class of structured multi-dimensional Markov processes whose state space can be partitioned into two parts: a finite set of boundary states and a structured…
Fluctuations in stochastic systems are usually characterized by the full counting statistics, which analyzes the distribution of the number of events taking place in the fixed time interval. In an alternative approach, the distribution of…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet sizes (hence service…
This note presents conjectures on polynomial/algebraic/sub-exponential convergence of transition probabilities for $\lambda$-null recurrent and $\lambda$-transient Markov chains in continuous time. The only known positive examples are in…
A $M/M/1$ queue with catastrophes is a modified $M/M/1$ queue model for which, according to the times of a Poisson process, catastrophes occur leaving the system empty. In this work, we study a fractional $M/M/1$ queue with catastrophes,…
Consideration is given to the three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is…
This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale…
A new approach to the steady state detection in the uniformization method of solving continuous time Markov chains is introduced. The method is particularly useful in solving inhomogenous CTMC's in multiple steps, where the desired error…
The paper studies closed queueing networks containing a server station and $k$ client stations. The server station is an infinite server queueing system, and client stations are single-server queueing systems with autonomous service, i.e.…
In this paper, we consider five models of heavy-tailed queues involving Mittag-Leffler distributions that generalize the classical $M/M/1$ queues. These models are suitable modifications of previously defined models in such a way that the…
Recently, Atar and Miyazawa [2] introduced a multi-level GI/G/1 queue with a finite number of levels, where both the arrival and service rates depend on the level corresponding to the current queue length. For this model, they proved that…