Workers come to tool store room to enquire about special tools needed in a particular project. The average time between two arrivals is 40 secs and the arrivals are assumed to be in Poisson distribution. The average time of the tool room attendant is 30 secs. Determine (i) average queue length (ii) average length of non-empty queues (iii) average number of workers in system including the worker being attended (iv) mean waiting time of an arrival (v) average waiting time of an arrival, who waits (vi) whether additional number of tool store room attendants is needed to minimize the combined cost of attendant’s idle time and the cost of workers’ time.
Assume the charges of a skilled worker Rs. 15 per hour and that of tool store room attendant Rs. 4 per hour and also 8 working hours a day.