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 Si and the average number of visits that a customer makes to device i is Vi. For all customer populations n (1

Table 12.5. The MVA Algorithm

Initialize the average number of customers at each device i:

graphics/323fig05.gif(0) = 0)

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

calculate the average residence time for each device i:

graphics/323fig01.gif

calculate the overall system response time:

graphics/323fig02.gif

calculate the overall system throughput:

graphics/323fig03.gif

calculate the throughput for each device i:

Xi(n) = Vi x X0(n)

calculate the utilization for each device i:

Ui(n) = Si x Xi(n)

calculate the average number of customers at each device i:

graphics/323fig04.gif

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: (graphics/323fig05.gif(0) = 0).

graphics/324equ01.gif


For customer population n = 1, calculate the average residence time for each device i: (graphics/323fig01.gif.)

graphics/324equ02.gif


Calculate the overall system response time: graphics/324fig01.gif.

graphics/324equ03.gif


Calculate the overall system throughput: graphics/324fig02.gif.

graphics/324equ04.gif


Calculate the throughput for each device i: (Xi(n) = Vi x X0(n)).

graphics/324equ05.gif


Calculate the utilization for each device i: (Ui(n) = Si x Xi(n)).

graphics/324equ06.gif


Calculate the average number of customers at each device i: (graphics/325fig01.gif(n) = graphics/325fig02.gif.

graphics/325equ01.gif


For customer population n = 2, calculate the average residence time for each device i: (graphics/326fig01.gif).

graphics/325equ02.gif


Calculate the overall system response time: graphics/325fig04.gif.

graphics/325equ03.gif


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

graphics/325equ04.gif


Calculate the throughput for each device i: (Xi(n) = Vi x X0(n)).

graphics/325equ05.gif


Calculate the utilization for each device i: (Ui(n) = Si x Xi(n)).

graphics/325equ06.gif


Calculate the average number of customers at each device i: (graphics/325fig01.gif(n) = X0(n)x graphics/326fig07.gif).

graphics/326equ01.gif


For customer population n = 3, calculate the average residence time for each device i: (graphics/326fig01.gif(n) = Di[1 + ñi(n 1)]).

graphics/326equ02.gif


Calculate the overall system response time: (graphics/326fig05.gif).

graphics/326equ03.gif


Calculate the overall system throughput: graphics/327fig06.gif.

graphics/326equ04.gif


Calculate the throughput for each device i: (Xi(n) = Vi x X0(n)).

graphics/326equ05.gif


Calculate the utilization for each device i: (Ui(n) = Si x Xi(n)).

graphics/326equ06.gif


Calculate the average number of customers at each device i: (graphics/327fig01.gif).

graphics/327equ01.gif


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.



Performance by Design. Computer Capacity Planning by Example
Performance by Design: Computer Capacity Planning By Example
ISBN: 0130906735
EAN: 2147483647
Year: 2003
Pages: 166

Similar book on Amazon

flylib.com © 2008-2017.
If you may any questions please contact us: flylib@qtcs.net