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statistics are required, compute the time when the customer will leave, and add that departure to the set of events waiting to happen If the event is an arrival, we check for an available teller If there is none, we place the arrival in the line (queue) Otherwise, we give the customer a teller, compute the customer's departure time, and add the departure to the set of events waiting to happen The waiting line for customers can be implemented as a queue Because we need to find the next soonest event, the set of events should be organized in a priority queue The next event is thus an arrival or departure (whichever is sooner); both are easily available An event-driven simulation is appropriate if the number of ticks between events is expected to be large

The S-function integration introduces the following restrictions on the energies E " w', stemming from the fact that - 1 :$ cos 8 :$ 1:

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The main algorithmic item in a simulation is the organization of the events in a priority queue To focus on this requirement, we write a simple simulation The system we simulate is a nzodeni bank at a university computing center A modem bank consists of a large collection of modems For example, Florida International University (FIU) has 288 modems a\iailable for students A modem is accessed by dialing one telephone number If any of the 288 modems are available, the user is connected to one of them If all the modems are in use, the phone will give a busy signal Our simulation models the service provided by the modem bank The variables are the number of modems in the bank, the probability distribution that governs dial-in attempts, the probability distribution that governs connect time, and the length of time the simulation is to be run

The modem bank simulation is a simplified version of the bank teller simulation because there is no waiting line Each dial-in is an arrival, and the total time spent once a connection has been established is the service time By removing the waiting line, we remove the need to maintain a queue Thus we have only one data structure, the priority queue In Exercise 1418 you are asked to incorporate a queue; as many as L calls will be queued if all the modems are busy To simplify matters, we do not compute statistics Instead, we list each event as it is processed We also assume that attempts to connect occur at constant intervals; in an accurate simulation we would model this interarrival time by a random process Figure 144 shows the output of a simulation

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1 User 0 dials in at time 0 and connects for 1 minutes 2 User 0 hangs up at time 1 3 user 1 dials in at time 1 and connects for 5 minutes 4 user 2 dials in at time 2 and connects for 4 minutes 5 User 3 dials in at time 3 and connects for 11 minutes 6 user 4 dials in at time 4 but gets busy signal 7 user 5 dials in at time 5 but gets busy signal 8 user 6 dials in at time 6 but gets busy signal 9 User 1 hangs up at time 6 1 User 2 hangs up at time 6 0 11 User 7 dlals in at time 7 and connects for 8 minutes 12 User 8 dials in at time 8 and connects for 6 minutes 13 User 9 dials in at time 9 but gets busy signal 14 User 10 dials in at time 10 but gets busy signal 15 User 11 dials in at time 11 but gets busy signal 16 User 12 dials in at time 12 but gets busy signal 17 User 13 dials in at time 13 but gets busy signal 18 User 3 hangs up at time 14 19 User 14 dials in at time 14 and connects for 6 minutes 20 User 8 hangs up at time 14 21 User 15 dials in at time 15 and connects for 3 minutes 22 User 7 hangs up at time 15 23 User 16 dials in at time 16 and connects for 5 minutes 24 user 17 dials in at time 17 but gets busy signal 25 User 15 hangs up at time 18 26 User 18 dials in at time 18 and connects for 7 minutes Figure 144 Sample output for the modem bank simulation involving three modems: A dial-in is attempted every minute; the average connect time is 5 minutes; and the simulation is run for 18 minutes.

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