On large deviations in queuing systems

The main purpose of the article is to provide a simpler and more elementary alternative derivation of the large deviation principle for compound Poisson processes defined

Using estimated entropy in a queueing system with dynamic routing.

In this article we consider a discrete time two server queueing system with dynamic routing. We prove logarithmic asymptotics for the liklihood that a message from a source that divides its messages between the two servers in a way that minimizes the message's waiting time experiences a large waiting time. We demonstrate the merit of this asymptotic by comparing its predictions with experimental data. We illustrate how estimated entropies of the traffic streams can be used to predict the likelihood of long waiting times and demonstrate the method's accuracy through comparison with simulations

Using estimated entropy in a queueing system with dynamic routing.

In this article we consider a discrete time two server queueing system with dynamic routing. We prove logarithmic asymptotics for the liklihood that a message from a source that divides its messages between the two servers in a way that minimizes the message's waiting time experiences a large waiting time. We demonstrate the merit of this asymptotic by comparing its predictions with experimental data. We illustrate how estimated entropies of the traffic streams can be used to predict the likelihood of long waiting times and demonstrate the method's accuracy through comparison with simulations

Using estimated entropy in a queueing system with dynamic routing.

In this article we consider a discrete time two server queueing system with dynamic routing. We prove logarithmic asymptotics for the liklihood that a message from a source that divides its messages between the two servers in a way that minimizes the message's waiting time experiences a large waiting time. We demonstrate the merit of this asymptotic by comparing its predictions with experimental data. We illustrate how estimated entropies of the traffic streams can be used to predict the likelihood of long waiting times and demonstrate the method's accuracy through comparison with simulations

Large deviations provide good approximation to queueing system with dynamic routing. Technical Paper DIAS-STP-04-15

We consider a system with two infinite-buffer FCFS servers (of speed one). The arrivals processes are three independent Poisson flows Ξi, of rates λi, i = 0; 1; 2, each with IID task service times. The tasks from Ξi are directed to server i; i = 1; 2 (dedicated traffic). The tasks from Ξ0 are directed to the server that has the shorter workload in the buffer at the time of arrival (opportunistic traffic). We compare the analytical data for the large deviation (LD) probabilities for the virtual waiting time in flow Ξ0 and empercial delay freqencies from simulations