Performance Modeling and Benchmarking of Event-Based ... - DVS

5.1. SPECJMS2007 - A STANDARD BENCHMARK 89
Interaction 6:
ξ6,a se = λ 6
ξ6,a re = λ 6 · |Ψ SM |
ξ j 6,k
= 0, ∀k ∈ Γ, k ≠ a ∧ j ∈ Ω
Interaction 7:
ξ7,a se = λ 7
ξ7,a re = λ 7 · |Ψ SM |
ξ j 7,k
= 0, ∀k ∈ Γ, k ≠ a ∧ j ∈ Ω
Message Throughput per Location We now analyze the message throughput on a per
location basis. The following notation will be used:
χ j l,k
for j ∈ Ω, l ∈ Λ, k ∈ Γ
No of messages of group k sent/received per sec by a location of type l.
χ j l = ∑ k∈Γ ξj l,k
for j ∈ Ω, l ∈ Λ
Total no of messages sent/received per sec by a location of type l.
SMs participate in all interactions apart from Interaction 2. The following equations characterize
the message throughput of each SM:
χ se
SM,a = χ se
SM,b = χ re
SM,c = 0
χ re
SM,a = λ 6 + λ 7
χ re
SM,b = λ 3
χ se
SM,c = λ 5
χ se
SM,d = 2λ 1 + λ 4
χ re
SM,d = 2λ 1 + λ 4
SPs participate only in Interaction 2. Overall λ 2 · |Ψ DC | callForOffers messages are sent
by the DCs per sec. Therefore, every SP receives ρ · λ 2 · |Ψ DC | messages and for each of them
it sends an offer to the respective DC. The probability that an offer is accepted is 1 ζ
and hence
the number of SP offers accepted per sec is given by:
ρ · λ 2 · |Ψ DC |
ζ
= λ 2 · |Ψ DC |
|Ψ SP |
The following equations characterize the message throughput of each SP:
χ se
SP,a = χ re
SP,a = χ se
SP,b = χ se
SP,c = χ re
SP,c = 0
χ re
SP,b = ρ · λ 2 · |Ψ DC |
χ se
SP,d = ρ · λ 2 · |Ψ DC | + 3λ 2 · |Ψ DC |
|Ψ SP |
χ re
SP,d = 2λ 2 · |Ψ DC |
|Ψ SP |
DCs participate in Interactions 1 and 2 both as producers and consumers of messages. The
number of SMs supplied by each DC is given by δ = |Ψ SM |
|Ψ DC | .