Queuing theory
1. 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
(1 Mark, 1997)

Ans: a
2. At a production machine, parts arrive according to a Poisson process at the rate of 0.35 parts per minute. Processing time for parts have exponential distribution with mean of 2 minutes. What is the probability that a random part arrival finds that there are already 8 parts in the system (in machine + in queue)?
(a) 0.0247
(b) 0.0576
(c) 0.0173
(d) 0.082
(2 Mark, 1999)

Ans: c
Explanation:
3. In a single server infinite population queuing model, arrivals follow a Poisson distribution with mean λ = 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) 5
(2 Mark, 2000)

Ans: b
Explanation:
4. 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
(2 Mark, 2002)

Ans: c
Explanation:
5. 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) 1/6 day
(b) 1/3 day
(c) 1 day
(d) 3 days
(2 Mark, 2004)

Ans: a
6. Consider a single server queuing model with Poisson arrivals (λ = 4 /hour) and exponential service (μ = 4 /hour) . 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) 1/11
(b) 1/10
(c) 1/9
(d) 1/2
(1 Mark, 2005)

Ans: a
Explanation:
7. 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
(1 Mark, 2006)

Ans: b
Explanation:
8. 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 \frac { { e }^{ \lambda T }{ (\lambda T) }^{ n } }{ n! }. The probability density function f(t) of the interarrival time is given by
(a) { \lambda }^{ 2 }({ e }^{ { \lambda }^{ 2 }t })
(b) \frac { { e }^{ { \lambda }^{ 2 }t } }{ { \lambda }^{ 2 } }
(c) { \lambda }({ e }^{ { \lambda }t })
(d) \frac { { e }^{ { \lambda }t } }{ { \lambda } }
(1 Mark, 2008)

Ans: c
9. 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
(1 Mark, 2010)

Ans: b
10. 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 steady state, the average waiting time in the queue is
(a) 10 minutes
(b) 20 minutes
(c) 25 minutes
(d) 50 minutes
(1 Mark, 2011)

Ans: d
Explanation:
11. 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
(1 Mark, 2013)

Ans: c
12. 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) 5/7
(b) 14/3
(c) 7/5
(d) 10/3
(2 Mark, 2014[1])

Ans: b
Explanation:
13. The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is
(a) Normal
(b) Poisson
(c) Erlang
(d) Beta
(1 Mark, 2014[1])

Ans: b
14. At a work station, 5 jobs arrive every minute. The mean time spent on each job in the work station is 1/8 minute. The mean steady state number of jobs in the system is _______.
(2 Mark, 2014[4])

Ans: 1.67
Explanation:
15. In the notation (a/b/c) : (d/e/f) for summarizing the characteristics of queuing situation, the letters ‘b’ and ‘d’ stand respectively for
(a) Service time distribution and queue discipline
(b) Number of servers and size of calling source
(c) Number of servers and queue discipline
(d) Service time distribution and maximum number allowed in system
(1 Mark, 2015[3])

Ans: a
16. In a singlechannel queuing model, the customer arrival rate is 12 per hour and the serving rate is 24 per hour. The expected time that a customer is in queue is _______ minutes.
(1 Mark, 2016[2])

Ans: 2.5
Explanation:
17. For a single server with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following service rates will provide a steady state finite queue length?
(a) 6 per hour
(b) 10 per hour
(c) 12 per hour
(d) 24 per hour
(1 Mark, 2017[2])

Ans: d
Explanation:
18. The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrival is between 1 and 3 minutes is _______. (correct to two decimal places).
(1 Mark, 2018[2])

Ans: 0.38
Explanation: