Summary: ISyE 6650 Exam # 2
Spring 2005
Name
Please be neat and show all your work so that I can give you partial credit.
GOOD LUCK.
Question 1
Question 2
Question 3
Total
1
(30) 1. Customers arrive according to a Poisson process with mean interarrival
time 1/. There are s servers in parallel and the service times are mutually in-
dependent exponentially distributed random variables with common mean 1/µ.
At time 0 all s servers are occupied and no customers are waiting.
(10)(a) Find the probability that the next arriving customer finds all the servers
busy.
(10) (b) Let N be the number of customers who arrive prior to the first service
completion. Find P{N = j} for j = 0, 1, 2, . . ..
(10) (c) Find the probability that the next arriving customer finds at least 2
idle servers.

Source: Ayhan, Hayriye - School of Industrial and Systems Engineering, Georgia Institute of Technology

Collections: Engineering