5.10 Trucks bring crates of goods to a warehouse that has a single attendant. It is the responsibility of each truck driver to offload his truck, and the time that it takes to offload a truck is exponentially distributed with mean 1=μ1. When a truck is offloaded, it leaves the warehouse and takes a time that is exponentially distributed with mean 1=λ to return to the warehouse with another set of crates. When a truck driver is done with offloading his truck, the warehouse attendant takes an additional time that is exponentially distributed with mean 1=μ2 to arrange the crates before the next truck in line can start offloading. Assume that there are N trucks that bring crates to the warehouse. Denote the state of the system by ðm; nÞ, where m is the number of trucks in the system and n is the state of the attendant: n 5 1 if the attendant is busy arranging the crates and n 5 0 otherwise.

a. Formulate the problem as a CTMC, specifying the state variables and giving the state-transition-rate diagram of the process.

b. From the diagram identify the steady-state probability that the attendant is idle with no truck in the warehouse.