Advances in Mobile Cloud Computing Systems

Modeling and Analysis of Single-Hop Mobile Cloudlet 251

where

β = λ

C

/(λ

I

+ λ

C

)

γ = λ

I

/(λ

I

+ λ

C

)

Subsequently,

E(N(τ)) = E(N(τ)|I

0

=0)p

0

+ E(N(τ)|I

0

=1)p

1

,

=

λ

I

λ

C

τ

λ

I

+ λ

C

+

p

0

λ

2

I

+ p

1

λ

2

C

(λ

I

+ λ

C

)

2

(1 −e

−(λ

I

+λ

C

)τ

), (6.13)

where

p

1

= πr

2

/(n/λ)

p

0

=1−p

1

The computing capacity of C

τ

satisfies

C

C

τ

≥

N(τ)



j=1

CT

j

(τ)S.

Therefore, E(C

C

τ

) is lower bounded by

C

l

C

τ

 E(N(τ))S



E(TCT(τ)) −E(

CT)∗



p

1

π

11

F

T

C

(τ)(E(N(τ)) + 1) + (p

0

+ p

1

π

10

)E(N(τ))



, (6.14)

where E(

CT)=E(T

C

·1

T

C

<ρ

)+ρP(T

C

≥ρ)=

1−e

−λ

C

ρ

λ

C

.

Figure 6.7 shows the numerical results of Theorem 6.3 by setting

ρ =0.1 s (typical packet transmission time in mobile wireless net-

works), n = 10, T

I

and T

C

are exponential random variables with

μ

T

I

=83