Example 4-17: Delay of lift loads on a building site Suppose that a single crane is available on a building site and that each lift requires three minutes including the time for attaching loads. Suppose further that the cumulative arrivals of lift loads at different time periods are as follows: 6:00-7:00 A.M. 4 per hour 7:00-8:00 A.M. 15 per hour 8:00-11:00 A.M. 25 per hour 12:00-4:00 PM. 4:00-6:00 PM. 6:00PM-6:00 A.M. 8 per hour 4 per hour 0 per hour 11:00-12:00 A.M. 5 per hour Using the above information of arrival and service rates 1. Find the cumulative arrivals and cumulative number of loads served as a function of time, beginning with 6:00 AM. 2. Estimate the maximum queue length of loads waiting for service. What time does the maximum queue occur? 3. Estimate the total waiting time for loads. 4. Graph the cumulative arrival and departure functions. The maximum service rate x-60 min/3 min per lift-20 lifts per minute. The detailed computation can be carried out in the Table 4-2, and the graph of A(t) and D() is given in Figure 4-10. Table 4-2 Computation of queue length and waiting time Period: Arrival rate Cumulative arrivals AT) Cumulative Departure departures Waiting Queue rate DXT) time 6-7:00 4 4 0 4 4 7-8:00 15 19 0 15 19 0 0 8-9:00 44 20 39 9-10:00 69 10 20 59 10 10-11:00 94 15 20 79 11-12:00 99 0 20 99 12-1:00 107 0 107 1-2:00 2-3:00 115 0 8 115 123 0 8 123 3-4:00 131 0 131 4-5:00 5-6:00 135 0 135 2000000 15 0 139 0 139 0 6-7:00 139 0 139 0 7-8:00 139 139 Total waiting time-30 Maximum queue-15 Solve Example 4-17 if each lift requires 5 minutes instead of 3 minutes