4. Consider a two-teller bank where each teller has its separate queue. Customers are allowed to...

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4. Consider a two-teller bank where each teller has its separate queue. Customers are allowed to jockey between queues at departure instances. Note that a customer only switches queues at departure instances and if the other queue is shorter. New arrivals join the shorter queue and choose queue 1 if both queues are of equal length. Let n1(t) and n2(t) denote the number of customers in the system in queues 1 and 2 at time t. The following customer inter-arrival times (Ai) and service times for tellers 1 (S1i) and tellers 2 (S2i) have been generated: A1 = 1.8, A2= 3.2, A3 = 1.1, A4 = 5.2, S11 = 2.1, S12= 1.6, S13 = 5.2, S14 = 0.8 and S21 = 4.9, S22=2.7, S23 = 4.3, S24 = 2.3. a. Assume that n1(0) = 2, n2(0) = 3 and that both servers have just started processing at time 0. Use the above inter-arrival times and server times to simulate the system for 10 minutes using the below. table: b. Find the time average number of total customers over 10 minutes. t Events 0 (A, S1, S2 Next Event ni(t) n₂(t) A₁ 3 2 4. Consider a two-teller bank where each teller has its separate queue. Customers are allowed to jockey between queues at departure instances. Note that a customer only switches queues at departure instances and if the other queue is shorter. New arrivals join the shorter queue and choose queue 1 if both queues are of equal length. Let n1(t) and n2(t) denote the number of customers in the system in queues 1 and 2 at time t. The following customer inter-arrival times (Ai) and service times for tellers 1 (S1i) and tellers 2 (S2i) have been generated: A1 = 1.8, A2= 3.2, A3 = 1.1, A4 = 5.2, S11 = 2.1, S12= 1.6, S13 = 5.2, S14 = 0.8 and S21 = 4.9, S22=2.7, S23 = 4.3, S24 = 2.3. a. Assume that n1(0) = 2, n2(0) = 3 and that both servers have just started processing at time 0. Use the above inter-arrival times and server times to simulate the system for 10 minutes using the below. table: b. Find the time average number of total customers over 10 minutes. t Events 0 (A, S1, S2 Next Event ni(t) n₂(t) A₁ 3 2

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