While short note on multi-channel queue with infinite customer population IPUB.E. (Prod) 2001 5. Assuming - 12 hr. u - Shr,e - 3.p. -0.056, calculate (O) the average time a customer is in the system, (i) the average number of customers in the system, (HD) whether any time would be saved for customers if the 3-channel system with service rate of 5th is replaced by a single channel system with an average service rate of 15hr. (Anx. (6) 25 min (a) 498 () 5 min) 6. A bank has two counters for withdrawals. One counter handles withdrawals of value less than 1,000 and the other counter 1,000 and above Analysis of service time shows an exponential distribution with mean service time of 6 minutes per customer for each counter Arrival of customers follows Poisson distribution with mean 8 per hour for the first counter and 5 per hour for the second counter (a) What are the average waiting times per customer of cach counter? (6) If cach counter could handle all withdrawals irrespective of their value, how would the average waiting time change? Kuru. U.BE (Mech) 1995) S24 Ans. (a) 24 min., 6 min. (b) 4.2 min) 7. A supermarket has two girls ringing up sales Y the counters. If the service time for each customer is exponential with mean 4 minutes, and if people arrive in a Poisson fashion at the rate of 10 hour, (a) What is the probability of having to wait for the service (b) What is the expected percentage of idle time for each girl? (c) Find the average queue length and the average number of units in the system. Chennai U. 2002) Ans (a) 0.167 (5) 6796.)