5.11 Consider a system consisting of two birth and death processes labeled system 1 and system 2. Customers arrive at system 1 according to a Poisson process with rate λ1, and customers arrive at system 2 according to a Poisson process with rate λ2. Each system has two identical attendants. The time it takes an attendant in system 1 to serve a customer is exponentially distributed with mean 1=μ1, and the time it takes an attendant in system 2 to serve a customer is exponentially distributed with mean 1=μ2. Any customer that arrives when the two attendants in its group are busy can receive service from the other group, provided that there is at least one free attendant in that group; otherwise it is lost. Let the state of the system be denoted by ðm; nÞ, where m is the number of customers in system 1 and n is the number of customers in system 2. Give the state-transition-rate diagram of the process and specify the probability that a customer receives service from a group that is different from its own group.