# At a single-phase, multiple-channel service facility, customers arrive randomly. Statistical analysi

At a single-phase, multiple-channel service facility, customers arrive randomly. Statistical analysis of past data shows that the interarrival time has a mean of 5 minutes and is exponentially distributed. The service time per customer has a mean of 4 minutes and is exponentially distributed. The arrival buffer capacity is 5 customers. The lost customer cost due to blocking is \$200 per customer. The waiting cost is \$100 per customer per hour. The server cost is \$20 per server per hour. Use Performance.xls spreadsheet for queue analysis and manual calculation for costs.

a. Find the optimal number of servers to be employed to minimize the total of lost customer cost, waiting cost, and server cost. (Ans: Cost per hour with one server=\$318.77; Cost with 2 servers = \$58.00; Cost with 3 servers = \$62.00: So two servers are optimal.)

b. Find the average overall waiting time and the average total flow time through the system for the optimal case. (Ans: Waiting time: 0.73 min; Flow time: 4.73 min)