U. Glaeser

The traditional load independent mean value analysis program (LIMVA) is based on assumption that
the service times of all servers are constant. The goal of MVA models is to compute system response
times, utilizations, and throughputs. Following is the traditional LIMVA model:
for n = 1 to N do
end_for
For perfectly balanced systems where all demands are equal (D = V1S1 = V2S2 = … = VK SK), this algorithm
yields equal distribution of jobs in service centers
This is a consequence of equal residence times:
Qk( 0)
= 0, k = 1,…,K
Rk( n)
= Sk[ 1 + Qk( n – 1)
], k = 1,…,K
K
∑
R( n)
= VkR k( n)
k=1
X( n)
= n/R( n)
Xk( n)
= Vk X( n),
k = 1,…,K
Uk( n)
= Sk Xk( n)
= Dk X( n),
k = 1,…,K
Qk( n)
= Vk X( n)Rk(
n),
k = 1,…,K
Qk( n)
= n/K, k = 1,…,K
Vk Rk( n)
= Dk[ 1 + Qk ( n – 1)
] = D[ 1 + ( n – 1)/K],
k = 1,…,K
and their use for computing Q k(n) = V k X(n)R k(n). Furthermore, this yields linear response times, and
other relations:
R( n)
= KVkRk( n)
= ( n – 1 + K)D
Rk( n)
= ( n – 1 + K)Sk/K,
k = 1,…,K
X( n)
= n/ ( n – 1 + K)D
Xk( n)
= n/ ( n – 1 + K)Sk,
k = 1,…,K
Uk( n)
= n/ ( n – 1 + K),
k = 1,…,K
Of course, in a general case we have different demands, and the response time is no longer linear.
Unfortunately, the nature of the LIMVA model is essentially quasi-linear. Even for different demands the
response time curves remain similar to straight lines.
Limitations of the LIMVA model are exemplified in Fig. 8.11. In this case the processor service time
obtained from measurements is S p = 825 µs, the number of processor visits per job is V p = 7000, yielding
processor demand D p = 5.775 s. The number of disks is 14 and the number of disk visits per job is V d =
7000/14 = 500. The available resources include the central processor and 14 equally loaded disk units. A
spectrum of LIMVA models can be obtained for disk service times varying in the range 12 ms ≤ S d ≤ 24 ms,
© 2002 by CRC Press LLC