Abstract
In this paper, the transient solution is obtained for a multiprocessor system with multiple Poisson streams of task and exponential execution times. Each task requires exactly one processor for its execution and the scheduling policy is FCFS. The scheduler schedules a newly arriving task into any one of the idle processors, and the task is rejected if there is no idle processor. For this model, the exact time-dependent solution of system size probabilities at various streams, their means, variances and correlations are obtained using the properties of tridiagonal determinants.
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