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TABLE 34.3 Balanced job Bounds for the System of Example 34.4

Responce Time
Throughput
N Lower
BJB
MVA Upper
BJB
Lower
BJB
MVA Upper
BJB

1 6.000 6.000 6.000 0.100 0.100 0.100
2 7.200 7.400 7.800 0.169 0.175 0.179
3 8.400 9.088 10.500 0.207 0.229 0.242
4 9.600 11.051 13.364 0.230 0.266 0.294
5 11.000 13.256 16.286 0.246 0.290 0.333
. . . . . . .
. . . . . . .
. . . . . . .
15 41.000 41.089 46.091 0.299 0.333 0.333
16 44.000 44.064 49.085 0.301 0.333 0.333
17 47.000 47.045 52.080 0.303 0.333 0.333
18 50.000 50.032 55.075 0.305 0.333 0.333
19 53.000 53.022 58.071 0.306 0.333 0.333
20 56.000 56.016 61.068 0.307 0.333 0.333


FIGURE 34.4  Balanced job bounds on the responce time and the throughput.

EXERCISES

34.1 A transaction processing system can be modeled by an open queueing network shown in Figure 32.1. The transactions arrive at a rate of 0.8 transactions per second, use 1 second of CPU time, make 20 I/O’s to disk A and 4 I/O’s to disk B. Thus, the total number of visits to the CPU is 25. The disk service times are 30 and 25 milliseconds, respectively. Determine the average number of transactions in the system and the average response time.

FIGURE 34.5
Model of a 2-hop computer network.

34.2 For the system of Exercise 33.6, use MVA to compute the system throughput and response time for N, =1,..., 5 interactive users.
34.3 Repeat Exercise 34.2 using Schweitzer’s approximation to MVA with N = 5 users. Use a starting value of for each of the three-device queue lengths and stop after five iterations.
34.4 A 2-hop computer network with a “flow control window size” of n is represented by the closed queueing network shown in Figure 34.5. Assuming that the network is balanced in that each computer takes the same service time S to process a packet and that each packet makes one visit to each queue, determine the network throughput and response time as a function of n for n = 1,...,5 using MVA. Write an expression for X(n) and R(n).
34.5 Repeat Exercise 34.4 for an h-hop computer network. Such a network will have h + 1 queues connected in a ring. Write an expression for “network power,” which is defined as the ratio of throughput to the response time. Determine the window size n that gives the maximum network power.
34.6 Write the expressions for balanced bounds on the system throughput and response time of the system of Exercise 33.6 and compute the bounds for up to N = 5 users.
34.7 Consider a balanced, closed queueing network consisting of M fixed-capacity service centers (no terminals). The service demand on each center is Di = D/M. For this system:
a. Using MVA, develop an expression for the throughput and response time of the system as a function of the number of jobs N in the network.
b. Write expressions for balanced job bounds on the system throughput and response times for this system.
c. Verify that the bounds are tight in the sense that both upper and lower bounds are identical. Also, verify that the bounds are equal to the exact value obtained using MVA.


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