Chapter 9.9, Problem 25P

(a)

Summary Introduction

Interpretation:The expected flow time in the system is to be estimated assuming FCFS processing discipline.

Concept Introduction:

The following formula will be used −

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

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

(b)

Summary Introduction

Interpretation:The probability that any job waits more than 30 minutes for processing under FCFS is to be computed.

Concept Introduction:

The following formula will be used −

  $P\{W>t\}=e^{-(\mu -\lambda )t}$

Where,

t = time

  $\text{λ=Mean arrival time}$

  $\text{σ=Service time}$

(c)

Summary Introduction

Interpretation:The probability that the job waits more than 30 minutes for processing under LCFS is to be determined using normal approximation.

Concept Introduction:

The following formula will be used −

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

  ${\text{P}}_{\text{LCFS}}\left\{\text{W>}\text{1}/\text{2}\right\}\text{=P}\left\{\text{z>}\frac{\left({\text{required time-(E}}_{\text{FCFS}}\text{(W)))}\right)}{\text{Std}{\text{. deviation}}_{\text{LCFS}}\text{(W)}}\right\}$