1
GATE ME 2014 Set 1
+2
-0.6
Jobs arrive at a facility at an average rate of $$5$$ in an $$8$$ hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is $$40$$ minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be
A
$${5 \over 7}$$
B
$${14 \over 3}$$
C
$${7 \over 5}$$
D
$${10 \over 3}$$
2
GATE ME 2004
+2
-0.6
A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a ‘first come first served’ queue discipline. Breakdowns occur on an average of $$3$$ per day with a range of zero to eight. The maintenance crew can service an average of $$6$$ machines per day with a range of zero to seven. The mean waiting time for an item to be serviced would be
A
$${1 \over 6}$$ day
B
$${1 \over 3}$$ day
C
$$1$$ day
D
$$3$$ day
3
GATE ME 2002
+2
-0.6
Arrivals at a telephone booth are considered to be Poisson, with an average time of $$10$$ minutes between successive arrivals. The length of a phone call is distributed exponentially with mean $$3$$ minutes. The probability that an arrival does not have to wait before service is
A
$$0.3$$
B
$$0.5$$
C
$$0.7$$
D
$$0.9$$
4
GATE ME 2000
+2
-0.6
In a single server infinite population queuing model, arrivals follow a Poisson distribution with mean $$\lambda = 4$$ per hour. The service times are exponential with mean service time equal to $$12$$ minutes. The expected length of the queue will be
A
$$4$$
B
$$3.2$$
C
$$1.25$$
D
$$24.3$$
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