A scheduling approach to harness synergy from two server farms

In this paper, we first consider two multi-server M/M/K/FCFS queuing systems, processing two classes of jobs one-on-one respectively. We then operate the two multi-server systems as preemptive-resume priority queues (M/M/K/Prio) and route the two classes of jobs to both systems by splitting the Poisson arrivals of each class probabilistically. In each M/M/K/Prio system, own class of jobs are serviced with high priority while class of jobs routed from other system are serviced with low priority. Through numerical computations, we show that for a Pareto set of split probabilities, the probability of wait for service in queues experienced by both classes of jobs in the joint M/M/K/Prio systems, can be less than what they experienced in the original one-on-one M/M/K/FCFS systems. Through Bargaining theory, we capture the agreement of arrival load split between the two systems.