1 The M/G/1 Queue Recall that an M/G/1 queue consists of a single server who receives customers at the times of a Poisson process at rate λ > 0 that wait in line to be served on a sequential basis in order of arrival. The i-th customer comes with a workload for the server given by the random variable ξi. The quantities {ξi : i ≥ 1} are i.i.d. The server processes incoming work at a constant (un...

We model competition between two firms selling identical goods to customers who arrive in the market stochastically. Shoppers choose where to purchase based upon both price and the time cost associated with waiting for service. One seller provides two separate queues, each with its own server, while the other seller has a single queue and server. We explore the market impact of the multi-server...

A“scheduled” arrival process is one in which the nth scheduled for time n, but instead occurs at \(n+\xi _n\) , where \(\xi _j\)’s are i.i.d. We describe here behavior of a single server queue fed by such traffic processing times deterministic. A particular focus on perturbations with Pareto-like tails finite mean. obtain tail approximations steady-state workload both cases critically loaded an...