1
GATE ME 2013
+1
-0.3
Customers arrive at a ticket counter at a rate of $$50$$ per hr 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
$$3$$
B
$$4$$
C
$$5$$
D
$$6$$
2
GATE ME 2011
+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
3
GATE ME 2010
+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
4
GATE ME 2008
+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
$${{{{e^{ - \lambda t}}} \over \lambda }}$$
GATE ME Subjects
Engineering Mechanics
Strength of Materials
Theory of Machines
Engineering Mathematics
Machine Design
Fluid Mechanics
Turbo Machinery
Heat Transfer
Thermodynamics
Production Engineering
Industrial Engineering
General Aptitude
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Joint Entrance Examination