Evsey Morozov

Stability analysis of multiserver discrete-time queueing systems with renewal-type server interruptions

For many queueing systems, the server is not continuously available. Service interruptions may result from repair times after server failures, planned maintenance periods or periods during which customers from other queues are being served. These service interruptions cause an overall performance degradation which is most striking when interruptions can start while a customer is being served and his service has to start all over after the interruption. This is the so-called preemptive repeat service discipline. This paper investigates stability conditions for discrete-time queueing systems with preemptive server interruptions. Under renewal assumptions for arrival, service and interruption processes, sufficient conditions for the positive recurrence of the single-server and multiserver queueing processes are established for the preemptive repeat different and the preemptive resume service disciplines.

Stability of single‐wavelength optical buffers

Optical burst switching (OBS) provides a future-proof alternative to the current electronic switching in the backbone, but has buffering implemented with a set of fiber delay lines (FDLs). The resulting buffering system fundamentally differs from a classic one, in that the set of possible waiting times is not a continuum (like in the classic case) but rather a denumerable set, each value corresponding to the length of a delay line. As a result, arriving bursts in general have to wait longer than they would in a classic buffer, since their waiting time has to be in that denumerable set. The additional delay results in overall longer waiting times, when compared to a classic infinite buffer system with a continuous waiting room. While previous work already focused on the performance evaluation of finite optical buffers, the stability problem of the infinite system received only little attention. This contribution is the first to present a complete proof of sufficient stability conditions in the case of a general infinite FDL set, general arrival process and general service times. The key elements of analysis is the exploiting of the regenerative property of the waiting-time process and a characterisation of the limiting forward renewal time process. The given bound on the traffic load guarantees stability for a wide class of GI/G/1 optical buffers, and poses no restriction on the FDL lengths. Copyright

STABILITY ANALYSIS AND SIMULATION OF N-CLASS RETRIAL SYSTEM WITH CONSTANT RETRIAL RATES AND POISSON INPUTS

In this paper, we study a new retrial queueing system with N classes of customers, where a class-i blocked customer joins orbit i. Orbit i works like a single-server queueing system with (exponential) constant retrial time (with rate

Stability analysis of cascade networks via fluid models

\mu_{0}^{(i)}

Stability of multiwavelength optical buffers with delay‐oriented scheduling

) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance wireless multi-access systems, and transmission control protocols. First, we present a review of some corresponding recent results related to a single-orbit retrial system. Then, using a regenerative approach, we deduce a set of necessary stability conditions for such a system. We will show that these conditions have a very clear probabilistic interpretation. We also performed a number of simulations to show that the obtained conditions delimit the stability domain with a remarkable accuracy, being in fact the (necessary and sufficient) stability criteria, at the very least for the 2-orbit M/M/1/1-type and M/Pareto/1/1-type retrial systems that we focus on.

Accelerated verification of stability of simultaneous service multiserver systems

In this work, the fluid approach methodology is first applied to find a sufficient stability condition for a two-station cascade network: customers that are awaiting service at the first queue can move to the second station, whenever it is free, to be served there immediately, but the opposite is not allowed. Each station is fed by a renewal input with general i.i.d. inter-arrival times and general i.i.d. service times (possibly different in the two stations). Then we extend the stability analysis to cascade networks with an arbitrary number N of stations and find a sufficient stability condition. In such networks, an awaiting customer from the queue j ? N - 1 jumps to station j + 1 if free, to be served there. Finally, we obtain a necessary condition for stability of the N -station cascade network, which matches the sufficient condition when N = 2 .

A State-Dependent Control for Green Computing

This contribution presents the first stability analysis of multiwavelength queueing systems. Results are obtained for a wide class of implementable scheduling disciplines referred to as delay-oriented disciplines, a class to which for example join the shortest queue belongs. Scheduling is applied as contention resolution in optical switches accommodated with fibre delay lines as means of buffering. The analysis yields sufficient stability conditions for multiwavelength optical buffers with a general fibre-delay-line set, renewal input and general service times. Copyright

Regenerative analysis of a finite buffer fluid queue

We propose a new approach which allows to accelerate verification of the stability criterion of a multiserver model with simultaneous service for large number of servers. This approach reduces a state space related to calculation of a basic normalization constant included in the stability condition. Moreover, this result allows to obtain a stable configuration of the supercomputers with a given input rate.

Stability Analysis of a Basic Collaboration System via Fluid Limits

In this paper, we consider a state-dependent mechanism which can be used to reduce mean power consumption in modern communication and computer systems. This mechanism allows to change flexibly the service rate so as to increase the energy efficiency of the system. We focus on computer systems with sojourn time dependent service rate, and present a new regenerative proof of the sufficient stability conditions for a wide class of such systems. We develop both performance analysis in stationary regime and asymptotic analysis of the mean power consumption as the switching threshold increases. Some numerical results are presented and discuss in detail.

Monotonicity and stochastic bounds for simultaneous service multiserver systems

We discuss the application of the regenerative simulation of estimate the loss probability in a queueing system with finite buffer which is fed by a Gaussian input. We mainly consider queue with Brownian input. Stability analysis is discussed and some numerical examples are also included.