MAP 6264 Homework 6 ( M/D/1/n ) 20 Points Repeat Homework 5, but now assume that the service times are constant: Consider the M/D/1/n queue (finite waiting room, that is, a buffer with n waiting positions). Write a simulation program for this model, and compare the simulation results with the predictions of queueing theory. Specifically, let W(n) denote the average waiting time (in units of average service time) for those customers who receive service (that is, those customers who do not overflow the buffer) when the capacity of the buffer is n; and fill in the tables. In the first case, take a = 0.8 erlangs; in the second case, take a = 1.2 erlangs. Show the simulation code and output. Explain all theoretical calculations. Case 1 ρ Πn+1 W (n) n theory simulation theory simulation theory simulation 0 1 2 4 8 16 32 ∞ Case 2 ρ Πn+1 W (n) n theory simulation theory simulation theory simulation 0 1 2 4 8 16 32 ∞ MAP 6264 Homework 7 ( D/M/1/n ) 20 Points Repeat Homework 5, but now assume that the interarrival times are constant: Consider the D/M/1/n queue (finite waiting room, that is, a buffer with n waiting positions). Write a simulation program for this model, and compare the simulation results with the predictions of queueing theory. Specifically, let W(n) denote the average waiting time (in units of average service time) for those customers who receive service (that is, those customers who do not overflow the buffer) when the capacity of the buffer is n; and fill in the tables. In the first case, take a = 0.8 erlangs; in the second case, take a = 1.2 erlangs. Show the simulation code and output. Explain all theoretical calculations. Case 1 n ρ Πn+1 W (n) theory simulation theory simulation theory simulation 0 5 10 20 30 ∞ Case 2 n ρ Πn+1 W (n) theory simulation theory simulation theory simulation 0 5 10 20 30 ∞ MAP 6264 Homework 5 ( M/M/1/n ) 20 Points Consider the M/M/1/n queue (finite waiting room, that is, a buffer with n waiting positions). Write a simulation program for this model, and compare the simulation results with the predictions of queueing theory. Specifically, let W(n) denote the average waiting time (in units of average service time) for those customers who receive service (that is, those customers who do not overflow the buffer) when the capacity of the buffer is n; and fill in the tables. In the first case, take a = 0.8 erlangs; in the second case, take a = 1.2 erlangs. Show the simulation code and output. Explain all theoretical calculations. Case 1 ρ Πn+1 W (n) n theory simulation theory simulation theory simulation 0 1 2 4 8 16 32 ∞ Case 2 ρ Πn+1 W (n) n theory simulation theory simulation theory simulation 0 1 2 4 8 16 32 ∞ MAP 6264 Homework 4 (Finite-Source Input, BCC) 30 Points Adapt the simulation program of Homework 1 (Blocked Customers Cleared) to account for finite-source input. Consider the three cases: 1. Exponential think times (quasirandom input), exponential service times. 2. Exponential think times, constant service times. 3. Constant think times, exponential service times. Assume that s = 10 servers; and, for each value of n (number of sources), calculate (offered load per idle source) so that (intended offered load) is 9.6 erlangs. Run each simulation for as many arrivals as necessary to attain statistical stability. When n = (in Case 1 and Case 2) use the simulation of Homework 1. (Note that for every value of n, the theory values are the same for each case, because of insensitivity of the equilibrium probabilities to the think times and the service times). Fill in the tables. Attach code for simulation and theory; and explain all calculations. a ˆ * a ∞ Ps[n] -------------------- simulation -------------------- n theory 1 2 3 10 11 12 13 14 15 25 50 100 1000 ∞Πs[n] -------------------- simulation -------------------- n theory 1 2 3 10 11 12 13 14 15 25 50 100 1000 ∞ ρ -------------------- simulation -------------------- n theory 1 2 3 10 11 12 13 14 15 25 50 100 1000 ∞