hw8_soln - Homework 8 Solution Set Question 1 a State of...

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Homework 8 Solution Set Question 1 a) State of the system B1: Server 1 busy B2: Server 2 busy N: Number of customers in the system (including the customers in the servers) Events Arrival Departure from server 1 Departure from server 2 b) Arrival event at time t N=N+1 Sample an interarrival time IA and schedule at arrival event at time t + IA If (B1=0) then B1=1 Sample a service time S1 and schedule a departure from server 1 at time t + S1 Else If (B2=0) B2=1 Sample a service time S2 and schedule a departure from server 2 at time t + S2 End If Departure event from server 1 at time t N=N-1 B1=0 If (N-B2 >= 1) then B1=1 Sample a service time S1 and schedule a departure from server 1 at time t + S1 End If Departure Event from Server 2 N=N-1 B2=0 If (N-B1 >= 1) B2=1 Sample a service time S2 and schedule a departure from server 2 at time t + S2 End If
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c) A represents an arrival event, D1 represents a departure from server 1, D2 represents a departure from server 2. (B1,B2,N) FEL Event Total time server 1 busy Total time server 2 busy Total time more than 1 0 (0,0,0) (E,10)(A,1.3) 0 0 0 1.3 (1,0,1) (E,10)(A,2.4)(D1,3.4) A 0 0 0 2.4 (1,1,2) (E,10)(A,3.0)(D1,3.4)(D2,4.6) A 1.1 0 0 3.0 (1,1,3) (E,10)(A,4.5)(D1,3.4)(D2,4.6) A 1.7 0.6 0 3.4 (1,1,2) (E,10)(A,4.5)(D1,4.7)(D2,4.6)
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