12.3 The MVA Algorithm

The MVA algorithm is given concisely in Table 12.5. This is for any single class network with N customers and K devices. The average service time of a customer at device i is S_i and the average number of visits that a customer makes to device i is V_i. For all customer populations n (1

Initialize the average number of customers at each device i:

(0) = 0)

For each customer population n = 1, 2,... N,

calculate the average residence time for each device i:

calculate the overall system response time:

calculate the overall system throughput:

calculate the throughput for each device i:

X_i(n) = V_i x X₀(n)

calculate the utilization for each device i:

U_i(n) = S_i x X_i(n)

calculate the average number of customers at each device i:

Applied to the database server example, where the average service times are 10 seconds, 15 seconds, and 30 seconds, respectively, for the CPU (cp), fast disk (fd), and slow disk (sd), and where the average number of visits to each device are 1.0, 0.5, and 0.5, the MVA iteration proceeds as follows:

Initialize the average number of customers at each device i: ((0) = 0).

For customer population n = 1, calculate the average residence time for each device i: (.)

Calculate the overall system response time: .

Calculate the overall system throughput: .

Calculate the throughput for each device i: (X_i(n) = V_i x X₀(n)).

Calculate the utilization for each device i: (U_i(n) = S_i x X_i(n)).

Calculate the average number of customers at each device i: ((n) = .

For customer population n = 2, calculate the average residence time for each device i: ().

Calculate the overall system response time: .

Calculate the overall system throughput: (X₀(n) = n/R(n)).

Calculate the throughput for each device i: (X_i(n) = V_i x X₀(n)).

Calculate the utilization for each device i: (U_i(n) = S_i x X_i(n)).

Calculate the average number of customers at each device i: ((n) = X₀(n)x ).

For customer population n = 3, calculate the average residence time for each device i: ((n) = D_i[1 + ñ_i(n 1)]).

Calculate the overall system response time: ().

Calculate the overall system throughput: .

Calculate the throughput for each device i: (X_i(n) = V_i x X₀(n)).

Calculate the utilization for each device i: (U_i(n) = S_i x X_i(n)).

Calculate the average number of customers at each device i: ().

These performance metrics found via MVA for two and three customers (i.e., when n = 2 and when n = 3) correspond directly to those found from first principles (i.e., by constructing the Markov model, forming the balance equations, solving the balance equations, and interpreting the results) as demonstrated in Section 12.2 and shown in Tables 12.1 and 12.4. The significant difference is that the amount of computation required using MVA is negligible. MVA easily scales to a high number of devices and a high number of customers.