Related papers: Local stability in a transient Markov chain
We consider a two station cascade system in which waiting or externally arriving customers at station $1$ move to the station $2$ if the queue size of station $1$ including a customer being served is greater than a given threshold level…
We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a certain Markov process. Such a stochastic system can be used as a model in a priority service system, especially when…
Queueing networks are gaining attraction for the performance analysis of parallel computer systems. A Jackson network is a set of interconnected servers, where the completion of a job at server i may result in the creation of a new job for…
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…
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 consider a single-server cyclic polling system with three queues where the server follows an adaptive rule: if it finds one of queues empty in a given cycle, it decides not to visit that queue in the next cycle. In the case of limited…
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit…
In this paper we establish a necessary and sufficient stability condition for a stochastic ring network. Such networks naturally appear in a variety of applications within communication, computer, and road traffic systems. They typically…
We consider a polling system with two queues, where a single server is attending the queues in a cyclic order and requires non-zero switching times to switch between the queues. Our aim is to identify a fairly general and comprehensive…
This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part…
A matching queue is described via a graph $G$ together with a matching policy. Specifically, to each node in the graph there is a corresponding arrival process of items which can either be queued, or matched with queued items in neighboring…
Network capacity region of multi-queue multi-server queueing system with random ON-OFF connectivities and stationary arrival processes is derived in this paper. Specifically, the necessary and sufficient conditions for the stability of the…
This paper presents a new condition for the existence of optimal stationary policies in average-cost continuous-time Markov decision processes with unbounded cost and transition rates, arising from controlled queueing systems. This…
This paper considers a parallel system of queues fed by independent arrival streams, where the service rate of each queue depends on the number of customers in all of the queues. Necessary and sufficient conditions for the stability of the…
In this paper we show that in a multiclass Markovian network with unit rate servers, the condition that the average load $\rho$ at every server is less than unity is indeed sufficient for the stability or positive recurrence for \emph{any}…
We consider stability and network capacity in discrete time queueing systems. Relationships between four common notions of stability are described. Specifically, we consider rate stability, mean rate stability, steady state stability, and…
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 study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the meta-stability phenomenon. Large enough finite symmetric networks…
From the perspective of probability, the stability of growing network is studied in the present paper. Using the DMS model as an example, we establish a relation between the growing network and Markov process. Based on the concept and…
This note introduces a piecewise-deterministic queueing (PDQ) model to study the stability of traffic queues in parallel-link transportation systems facing stochastic capacity fluctuations. The saturation rate (capacity) of the PDQ model…