Geometric tail of queue length of low‐priority customers in a nonpreemptive priority MAP/PH/1 queue

We consider a MAP/PH/1 queue with two priority classes and nonpreemptive discipline, focusing on the asymptotic behavior of the tail probability of queue length of low‐priority customers. A sufficient condition under which this tail probability decays asymptotically geometrically is derived. Numerical methods are presented to verify this sufficient condition and to compute the decay rate of the tail probability.