Consider the open network (referred to as the system) of two single-server queues, i.e., Q1 and Q2, at steady state. New customers arrive at rate λ and enter Q1. Customers leaving Q1 choose to enter Q2 with probability 1−p, or they re-enter Q1 otherwise (with probability p). Customers leaving Q2 choose to leave the system with probability 1 − q, or they return to Q1 otherwise (with probability q). The known paramenters are: λ, p, q, N1 (defined as the average number of customers in Q1) and T2 (defined as the average time spent by a customer while visiting Q2 once). Solutions must be reported as functions of these known paramenters only.

A) Compute λ1 and λ2 defined as the arrival rates into Q1 and Q2, respectively

B) Compute T1 defined as the customer’s average time spent in Q1 during one single visit and N2 defined as the average number of customers in Q2

C) Compute Ttot defined as the average total time a customer spends in the entire system (i.e., visiting the queues before leaving the system)