Question

Customers arrive at a ticket counter at a range of 50 per hour and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in min is

• A. 5
• B. 3
• C. 4
• D. 6

Answer 1

The correct option is A 5

$\text{Arrival rate,}\lambda =50\text{customer/hour}$

$=\frac{50}{60}=\frac{5}{6}\text{customer/minute}$

$\text{Service rate,}\mu =1\text{customer/minute}$

$\text{Average waiting time in queue,}$

$W_q=\frac{\lambda }{(\mu -\lambda )}=\frac{\frac{5}{6}}{1-(1-\frac{5}{6})}=5min$

$\text{Points to Remember :}$

$\text{Average waiting time in queue,}$

$W_q=\frac{L_q}{\lambda }=W_S-\frac{1}{\mu }=\frac{\lambda }{m(\mu -\lambda )}$

$\text{Average waiting time in system,}$
$W_S=\frac{L_S}{\lambda }=\frac{1}{(\mu -\lambda )}$