(Solved): Please show me only part c thank you :) 1) [22 pts.] In the central railway station 15 computerized ...

1) [22 pts.] In the central railway station 15 computerized reservation counters are available. A customer can book his/her ticket for any train on any day in any one of these computerized reservation counters. The average time spent per customer by each clerk is 5 minutes. Average arrivals per hour during three types of activity periods have been calculated and customers have been surveyed to determine how long they are willing to wait during each type of period. Type of period Arrivals / hour Customer's acceptable waiting time Peak 110 15 minutes Normal 60 10 minutes Low 30 5 minutes Making suitable assumptions on this queueing process, determine how many counters should be kept open during each type of period. Assumptions are given as follows: (1) Arrival of customers follows Poisson distribution with mean arrival rate 2. (2) Service time has exponential distribution with mean service rate u. (3) Service discipline is FCFS (4) The calling source (population) has infinite size. (5) Mean arrival rate at any reservation counter is less than the mean service rate (a<u). a) Is the system a multi-server system or not? b) Determine how many counters should be kept open during each type of period (peak, normal, low). c) Management decides to modify computerized reservation counters to show if they are busy (with red light on top) or free (green light on top). In this way, management will make a single queue for all computerized reservation counters. For the number of counters to be kept open during each type of period you found previously, calculate the improvements in customer's average waiting time during each type of period