Mumbai University > Electronics and Telecommunication > Sem5 > Random Signal Analysis

Marks: 5M

Year: May 2015

Relations between $L_s,L_q,W_s \ \ and \ \ W_q$

1. $L_s=λW_s$

2. $L_q=λW_q$

3. $W_s=W_q+\frac1{μ}$

   Multiplying by λ in above equation we get,

   $λW_s=λW_q+\fracλ{μ}$

4. ∴ $L_s=L_q+\frac{λ}μ$ (from 1, 2, 3)

Where,

$L_s$= expected(average) number of customers in the system or expected line length or expected queue size

$L_q$= expected (average) number of customers in the queue or average length of queue

$W_s$= expected (average) waiting time of a customer in the system

$W_q$= expected (average) waiting time of a customer in the queue

λ= mean arrival rate when $λ_n$ is constant for all n

μ= mean service rate when $μ_n$ is constant for all n≥1

Note:

• If any one of the above quantities is known, other three can be found out using the above relations

• Above relations hold good for the models with infinite capacity with slight change for the models with finite capacity.