1
GATE ME 2011
MCQ (Single Correct Answer)
+1
-0.3
Cars arrive at a service station according to Poisson's distribution with a mean rate of $$5$$ per hour. The service time per car is exponential with a mean of $$10$$ minutes. At state, the average waiting time in the queue is
A
$$10$$ min
B
$$20$$ min
C
$$25$$ min
D
$$50$$ min
2
GATE ME 2010
MCQ (Single Correct Answer)
+1
-0.3
Little’s law is relationship between
A
stock level and lead time in an inventory system
B
waiting time and length of the queue in a queuing system
C
number of machines and job due dates in a scheduling problem
D
uncertainty in the activity time and project completion time
3
GATE ME 2008
MCQ (Single Correct Answer)
+1
-0.3
In an $$M/M/1$$ queuing system, the number of arrivals in an interval of length $$T$$ is a Poisson random variable (i.e., the probability of there being $$n$$ arrivals in an interval of length $$T$$ is $${{{e^{ - \lambda T}}{{\left( {\lambda T} \right)}^n}} \over {n!}}$$). The probability density function $$f(t)$$ of the inter-arrival time is given by
A
$${\lambda ^2}\left( {{e^{ - {\lambda ^2}t}}} \right)$$
B
$$\left( {{{{e^{ - {\lambda ^2}t}}} \over {{\lambda ^2}}}} \right)$$
C
$$\lambda {e^{ - \lambda t}}$$
D
$${{{{e^{ - \lambda t}}} \over \lambda }}$$
4
GATE ME 2006
MCQ (Single Correct Answer)
+1
-0.3
The number of customers arriving at a railway reservation counter is Poisson distributed with an arrival rate of eight customers per hour. The reservation clerk at this counter takes six minutes per customer on an average with an exponentially distributed service time. The average number of the customers in the queue will be.
A
$$3$$
B
$$3.2$$
C
$$4$$
D
$$4.2$$
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