) Queueing: Consider a system of two servers where customers from outside the system arrive at Server 1 at a Poisson rate 4 and at Server 2 at a Poisson rate 5. The service rates for Servers 1 and 2 are respectively 8 and 10. A customer, upon completion of service at Server 1 is equally likely to go to Server 2 or leave the system (i.e., P11 = 0, P12 = 0.5); whereas a departure from Server 2 will go 25% of the time to Server 1 and will depart the system otherwise (i.e., P21 = 0.25, P22 = 0).
a. Draw a schematic of the system showing critical information; use Kendall’s notation to describe system characteristics.
b. Determine the average number of customers and total expected time in the system.
