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 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

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

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