An parallel system model with pure space sharing among rigid jobs

We analyze a parallel system with two identical servers and pure space sharing among rigid jobs. The parallel system is modelled as an M / M / 2 queue with two types of jobs. Jobs of one type are parallel ones and require two servers while jobs of the other type need one server to start execution. Analysis of the system leads to a quartic polynomial for which a real root inside the unit disk is located. This root is then used to derive closed-form expressions for the mean queue length, mean response time as well as mean utilization of the system. The maximal utilization of the servers is also found. In addition, we provide an approximation that simplifies the previously found exact but complex expressions and gives insight into the impact of different parameters on system performance. Numerical experiments are presented and our formulae are validated by simulation.