M/M/1 queue

A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson distribution with a...

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 fin...

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 $$1$$ $$min.$$...

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 tak...

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 ave...

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 exponentia...

People arrive at a hotel in a Poisson distributed arrival rate of $$8$$ per hour. Service time distribution is closely approximated by the negative exponential. The average service...

On the average $$100$$ customers arrive at a place each hour, and on the average the server can process $$120$$ customers per hour. What is the proportion of time the server is idl...