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

Marks: 5M

Year: May 2015

Service discipline: First come first served

M/G/1 Queuing System is a single-server queuing system with Poisson input, general service time distribution and unlimited number of waiting positions.

Thus, an M/G/1 system has the following characteristics:

1. There is a single server with a general service time distribution with mean

   Average service time for a customer $(\bar{x} )=E\bar{(x)}$ and second moment $x^2=E(\bar{x} ^2)$

   (The service rate is μ=1/xcustomers per time unit)

2. Customers arriving according a Poisson process with the arrival rate λ customers per time unit

3. Number of waiting positions = ∞

Formulas for M/G/1 Queueing system:

$$N=N_q+N_s,T=W+ \bar{x }, \ \ \bar{ x}=\frac{1}μ,ρ_0=1-ρ$$

Where N=Average number of customers in the system

$N_q$=Average number of customers in the queue

$N_s$=Average number of customers in the service facilities

W=Average waiting time spent in the queue by a customer

T=Average time spent in the system by a customer

$ρ=\frac{λ}μ$=offered load (offered traffic)