Chapter 9.9, Problem 24P

(a)

Summary Introduction

Interpretation:The variance of the flow time assuming FCFS, LCFS and random selection disciplines is to be determined.

Concept Introduction:

The following formula will be used −

  ${\text{Expected flow time(E}}_{\text{FCFS}}\text{(W))=}\frac{\text{1}}{\text{μ-λ}}$

  $E_{FCFS}(W^2)=Va{r}_{FCFS}(W)+{(E_{FCFS}(W))}^2$

  $E_{LCFS}(W^2)=\left(\frac{1}{1-\rho }\right)(E_{FCFS}(W^2))$

  $E_{RANDOM}(W^2)=\left(\frac{1}{1-\raisebox{1ex}{$\rho $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right)(E_{FCFS}(W^2))$

(b)

Summary Introduction

Interpretation:The probability that the flow time in system will exceeds 10 minutes in each given cases is to be estimated.

Concept Introduction:

The following formula will be used −

  $P\{W>t\}=e^{-(\mu -\lambda )t}$

Where,

t = time

  $\text{λ=Mean arrival time}$

  $\text{σ=Service time}$