Operation Research - Queuing System. Solve Manually.

Problem #2/ (M/M/C):(GD/N/--), CSN Example 15.6-6 In the consolidated cab company problem of Example 15.6-5, suppose that new funds cannot be secured to purchase additional cabs. The owner was advised by a consultant that one way to re duce the waiting time is for the dispatching office to inform new customers of potential excessive delay once the waiting list reaches 6 customers. This move is certain to get new customers to seek service elsewhere, but will reduce the waiting time for those on the waiting list. Assess the friend's advice. Limiting the waiting list to 6 customers is equivalent to setting N = 6 + 4 = 10 customers We are thus investigating the model (M/M/4):(GD/10/00), where a - 16 customers per hour and 4 - 5 rides per hour. The following input data provide the results in Figure 15.8. Lambda Mu System limit Source limit 16 4 infinity 10 The average waiting time, W., before setting a limit on the capacity of the system is 149 hour (9 minutes) (see Figure 15.7), which is about twice the new average of 075 hour (-4.5 minutes). This remarkable reduction is achieved at the expense of losing about 3.6% of po tential customers (Pie - 03574). However, this result does not reflect the effect of possible loss of stomer ontwill on the operation of the company. In Example 15.6-6, determine the following: (a) The expected number of idle cabs. (6) The probability that a calling customer will be the last on the list. (c) The limit on the waiting list if it is desired to keep the waiting time in the queue to below 3 minutes Problem #2/ (M/M/C):(GD/N/--), CSN Example 15.6-6 In the consolidated cab company problem of Example 15.6-5, suppose that new funds cannot be secured to purchase additional cabs. The owner was advised by a consultant that one way to re duce the waiting time is for the dispatching office to inform new customers of potential excessive delay once the waiting list reaches 6 customers. This move is certain to get new customers to seek service elsewhere, but will reduce the waiting time for those on the waiting list. Assess the friend's advice. Limiting the waiting list to 6 customers is equivalent to setting N = 6 + 4 = 10 customers We are thus investigating the model (M/M/4):(GD/10/00), where a - 16 customers per hour and 4 - 5 rides per hour. The following input data provide the results in Figure 15.8. Lambda Mu System limit Source limit 16 4 infinity 10 The average waiting time, W., before setting a limit on the capacity of the system is 149 hour (9 minutes) (see Figure 15.7), which is about twice the new average of 075 hour (-4.5 minutes). This remarkable reduction is achieved at the expense of losing about 3.6% of po tential customers (Pie - 03574). However, this result does not reflect the effect of possible loss of stomer ontwill on the operation of the company. In Example 15.6-6, determine the following: (a) The expected number of idle cabs. (6) The probability that a calling customer will be the last on the list. (c) The limit on the waiting list if it is desired to keep the waiting time in the queue to below 3 minutes