Metastability of Queuing Networks with Mobile Servers

We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the meta-stability phenomenon. Large enough finite symmetric networks on regular graphs are proved to be transient for arbitrarily small inflow rates. However, the limiting non-linear Markov process possesses at least two stationary solutions. The proof of transience is based on martingale techniques

The analysis of batch sojourn-times in polling systems

We consider a cyclic polling system with general service times, general switch-over times, and simultaneous batch arrivals. This means that at an arrival epoch, a batch of customers may arrive simultaneously at the different queues of the system. For the exhaustive service discipline, we study the batch sojourn-time, which is defined as the time from an arrival epoch until service completion of the last customer in the batch. We obtain exact expressions for the Laplace–Stieltjes transform of the steady-state batch sojourn-time distribution, which can be used to determine the moments of the batch sojourn-time and, in particular, its mean. However, we also provide an alternative, more efficient way to determine the mean batch sojourn-time, using mean value analysis. We briefly show how our framework can be applied to other service disciplines: locally gated and globally gated. Finally, we compare the batch sojourn-times for different service disciplines in several numerical examples. Our results show that the best performing service discipline, in terms of minimizing the batch sojourn-time, depends on system characteristics