1
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
$${{{{e^{ - \lambda t}}} \over \lambda }}$$
2
GATE ME 2006
+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
$$4.2$$
3
GATE ME 2005
+1
-0.3
Consider a single server queuing model with Poisson arrivals $$\left( {\lambda = 4/hour} \right)$$ and exponential service $$\left( {\mu = 4/hour} \right)$$. The number in the system is restricted to a maximum of $$10.$$ The probability that a person who comes in leaves without joining the queue is
A
$${1 \over {11}}$$
B
$${1 \over {10}}$$
C
$${1 \over {9}}$$
D
$${1 \over {2}}$$
4
GATE ME 1997
+1
-0.3
The cost of providing service in a queuing system increases with
A
Increased mean time in the queue
B
Increased arrival rate
C
Decreased mean time in the queue
D
Decreased arrival rate
GATE ME Subjects
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Medical
NEET