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

88 CHAPTER 5. BENCHMARKING OF EVENT-BASED SYSTEMS
Table 5.3. Further, we define the following sets:
Γ = {a, b, c, d}
Ω = {se, re}
Message groups as defined in Table 5.3.
Messages sent vs. messages received.
Λ = {SM, SP, DC, HQ}
Types of physical locations.
Message Throughput per Interaction We first analyze the message throughput on a per
interaction basis. We will use the following notation:
ξ j i,k
for j ∈ Ω, 1 ≤ i ≤ 7 and k ∈ Γ
No of messages of group k sent/received per sec as part of Interaction i.
ξ j i = ∑ k∈Γ ξj i,k
for 1 ≤ i ≤ 7, j ∈ Ω
Total no of messages sent/received per sec as part of Interaction i.
ξ j = ∑ 7
i=1 ξj i for j ∈ Ω
Total no of messages sent/received per sec over all interactions.
Based on the information provided in the previous sections and analysis of the benchmark
design, the following equations are derived characterizing the message throughput of each interaction:
Interaction 1:
ξ1,c se = ξ1,c re = λ 1 · |Ψ SM |
ξ1,d se = ξ1,d re = 5 · λ 1 · |Ψ SM |
ξ j 1,k
= 0, ∀k ∈ {a, b} ∧ j ∈ Ω
Interaction 2: ξ j 2,a = 0, ∀j ∈ Ω
ξ2,b se = λ 2 · |Ψ DC |
ξ2,b re = ζ · λ 2 · |Ψ DC |
ξ2,c se = ξ2,c re = λ 2 · |Ψ DC |
ξ2,d se = ξ2,d re = (ζ + 5) · λ 2 · |Ψ DC |
Interaction 3:
ξ3,b se = λ 3
ξ3,b re = λ 3 · |Ψ SM |
ξ j 3,k
= 0, ∀k ∈ Γ, k ≠ b ∧ j ∈ Ω
Interaction 4:
ξ se
4,d = ξ re
4,d = λ 4 · |Ψ SM |
ξ j 4,k
= 0, ∀k ∈ Γ, k ≠ d ∧ j ∈ Ω
Interaction 5:
ξ se
5,d = ξ re
5,d = λ 5 · |Ψ SM |
ξ j 5,k
= 0, ∀k ∈ Γ, k ≠ d ∧ j ∈ Ω