Related papers: Large closed queueing networks in semi-Markov envi…
The paper studies a closed queueing network containing two types of node. The first type (server station) is an infinite server queueing system, and the second type (client station) is a single server queueing system with autonomous…
In this paper the infinite server queue model in semi-Markov random environment with k Markov arrival streams, random resources of customers, and catastrophes is considered. After catastrophes occur, all customers in the model are flashed…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…
We investigate the transient and stationary queue-length distributions of a class of service systems with correlated service times. The classical $M^X/G/1$ queue with semi-Markov service times is the most prominent example in this class and…
We consider the queuing networks, which are made from servers, exchanging their positions. The customers, using the network, try to reach their destinations, which is complicated by the movements of the servers, taking their customers with…
A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depends on the queue length. We…
This paper examines a discrete-time queuing system with applications to telecommunications traffic. The arrival process is a particular Markov modulated process which belongs to the class of discrete batched Markovian arrival processes. The…
We study a queueing network with a single shared server, that serves the queues in a cyclic order according to the gated service discipline. External customers arrive at the queues according to independent Poisson processes. After…
We study positive recurrence and transience of a two-station network in which the behavior of the server in each station is governed by a Markov chain with a finite number of server states; this service process can represent various service…
In this paper, we consider a $G_t/G_t/\infty$ infinite server queueing model in a random environment. More specifically, the arrival rate in our server is modeled as a highly fluctuating stochastic process, which arguably takes into account…
This paper studies a scheduling control problem for a single-server multiclass queueing network in heavy traffic, operating in a changing environment. The changing environment is modeled as a finite state Markov process that modulates the…
In the present paper the infinite-server MMAPkGk queueing model with random resource vector of customers, marked MAP arrival and semi-Markov (SM) arrival of catastrophes is considered. The joint generating functions (PGF) of transient and…
This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix $Q\equiv(q_{ij})_{i,j=1}^d$. Both arrival rates and service rates are depending on…
This paper studies a closed queueing network containing a hub (a state dependent queueing system with service depending on the number of units residing here) and $k$ satellite stations, which are $GI/M/1$ queueing systems. The number of…
The mathematics of the finite single server queue with Poisson input and semi-Markov service times($M/SM/1/b$) is similar to that used for $BMAP/G/1/b$ systems. This observation results in new analytical formulas for a queue size in the…
We consider the so-called GI/GI/N queueing network in which a stream of jobs with independent and identically distributed service times arrive according to a renewal process to a common queue served by $N$ identical servers in a…
A many-server queueing system is considered in which customers arrive according to a renewal process and have service and patience times that are drawn from two independent sequences of independent, identically distributed random variables.…
In this paper we analyze a single server queue with batch arrivals and semi-Markovian service times. We also include the feature that the first service of each busy period might have a different distribution than subsequent service times.…
We develop randomized modifications of Markov chains and apply these modifications to the routing chains of customers in Jacksonian stochastic networks. The aim of our investigations is to find new rerouting schemes for non standard Jackson…
Demand for studying queueing systems with multiple servers providing correlated services was created about 60 years ago, motivated by various applications. In recent years, the importance of such studies has been significantly increased,…