Stability of spatial queueing systems

Stability of queueing networks

2 The classical networks 186 2.1 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 2.2 Stationarity and reversibility . . . . . . . . . . . . . . . . . . . . 191 2.3 Homogeneous nodes of Kelly type . . . . . . . . . . . . . . . . . . 195 2.4 Symmetric nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 2.5 Quasi-reversibility . . . . . . . . . . . . . . . ...

Stability of Parallel Queueing Systems with Coupled Service Rates

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 system are derived, based on stochastic monotonicity and marginal drift properties of multiclass birth and death processes. These conditions yield a sharp ch...

Stability and Control of Piecewise-Deterministic Queueing Systems

We consider a piecewise-deterministic queueing (PDQ) model to study traffic queues due to stochastic capacity fluctuations in transportation facilities. The saturation rate (capacity) of the PDQ model switches between a finite set of values (modes) according to a Markov chain. The inflow to the PDQ is controlled by a state-feedback policy. The main results of this article are stability conditio...

Stochastic Stability of Queueing Networks*

This paper investigates geometric stability and L p-stability of discrete-time Markov chains associated with closed and open queueing networks with Markovian routing. By geometric stability (resp. L p-stability) we mean that the chain is re-generative in the Harris-recurrent sense and that the times between the successive regeneration points have a bounded moment generating function (resp. a bo...

Queueing Systems