Large deviations for the total queue size in non-Markovian tandem queues

Large deviations for the total queue size in non-Markovian tandem queues

We consider a d-node tandem queue with arrival process and light-tailed service processes at all queues i.i.d. and independent of each other. We consider three variations of the probability that the number of customers in the system reaches some high level N , namely during a busy cycle, in steady state, and upon arrival of a new customer. We show that their decay rates for large N have the sam...

Large Deviations for Join the Shorter Queue

Large-Deviations Analysis of the Fluid Approximation for a Controllable Tandem Queue

A fluid approximation gives the main term in the asymptotic expression of the value function for a controllable stochastic network. The policies which have the same asymptotic of their value functions as the value function of the optimal policy, are called asymptotically optimal policies. We consider a problem of finding from this set of asymptotically optimal policies a best one in the sense t...

Large Deviations for Markovian Nonlinear Hawkes Processes

In the 2007 paper, Bordenave and Torrisi [1] proves the large deviation principles for Poisson cluster processes and in particular, the linear Hawkes processes. In this paper, we prove first a large deviation principle for a special class of nonlinear Hawkes process, i.e. a Markovian Hawkes process with nonlinear rate and exponential exciting function, and then generalize it to get the result f...

Large deviations of the sojourn time for queues in series

We consider an open queueing network consisting of an arbitrary number of queues in series. We assume that the arrival process into the rst queue and the service processes at the individual queues are jointly stationary and ergodic, and that the mean inter-arrival time exceeds the mean service time at each of the queues. Starting from Lindley's recursion for the waiting time, we obtain a simple...