A G/M/1G/M/1 queueing system with PλM-service policy

We consider a G/M/1G/M/1 queue with PλM-service policy, which is a two-stage service policy. The stationary distribution of the workload under the policy is obtained through a decomposition technique and the analogy of level-crossings of the corresponding M/G/1M/G/1 queueing system.