For the single-server queueing system in Sec. 1.4, define L(t) to be the total number of c...

For the single-server queueing system in Sec. 1.4, define L(t) to be the total number of customers in the system at time t (including the queue and the customer in service at time t, if any).

(a) Is it true that L(t) = Q(t) + 1? Why or why not?

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(b) For the same realization considered for the hand simulation in Sec. 1.4.2, make a plot of L(t) vs. t (similar to Figs. 1.5 and 1.6) between times 0 and T(6).

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(c) From your plot in part (b), compute = the time-average number of customers in the system during the time interval [0, T(6)]. What is estimating?

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(d) Augment Fig. 1.7 to indicate how is computed during the course of the simulation.

FIGURE 1.5 Q(t), arrival times, and departure times for a realization of a single-server queueing system.

FIGURE 1.6 B(t), arrival times, and departure times for a realization of a single-server queueing system (same realization as in Fig. 1.5).

FIGURE 1.7 Snapshots of the system and of its computer representation at time 0 and at each of the 13 succeeding event times.