Sample path large deviations for multiclass feedforward queueing networks in critical loading

We consider multiclass feedforward queueing networks with first in first out and priority service disciplines at the nodes, and class dependent deterministic routing between nodes. The random behavior of the network is constructed from cumulative arrival and service time processes which are assumed to satisfy an appropriate sample path large deviation principle. We establish logarithmic asymptotics of large deviations for waiting time, idle time, queue length, departure and sojourn-time processes in critical loading. This transfers similar results from Puhalskii about single class queueing networks with feedback to multiclass feedforward queueing networks, and complements diffusion approximation results from Peterson. An example with renewal inter arrival and service time processes yields the rate function of a reflected Brownian motion. The model directly captures stationary situations.Comment: Published at http://dx.doi.org/10.1214/105051606000000439 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Delay analysis of a discrete-time multiclass slot-bound priority system

This paper introduces a new priority mechanism in discrete-time queueing systems that compromises between rst-come-rst-served (FCFS) and head-of-line (HoL) priority. In this scheduling discipline - which we dubbed slot-bound priority - customers of dierent priority classes entering the system during the same time-slot are served in order of their respective priority class. Customers entering during dierent slots are served on a FCFS basis. In this paper we study the delay in anN-class discrete-time queueing system under slot-bound priority. General independent arrivals and class-specic general service time distributions are assumed. Expressions for the probability generating function of the delay of a random type-jcustomer are derived, from which the respective moments are easily obtained. The tail behaviour of these distributions is analyzed as well, and some numerical examples show the eect slot-bound priority can have on the performance measures

Transient bayesian inference for short and long-tailed GI/G/1 queueing systems

In this paper, we describe how to make Bayesian inference for the transient behaviour and busy period in a single server system with general and unknown distribution for the service and interarrival time. The dense family of Coxian distributions is used for the service and arrival process to the system. This distribution model is reparametrized such that it is possible to define a non-informative prior which allows for the approximation of heavytailed distributions. Reversible jump Markov chain Monte Carlo methods are used to estimate the predictive distribution of the interarrival and service time. Our procedure for estimating the system measures is based in recent results for known parameters which are frequently implemented by using symbolical packages. Alternatively, we propose a simple numerical technique that can be performed for every MCMC iteration so that we can estimate interesting measures, such as the transient queue length distribution. We illustrate our approach with simulated and real queues