Introduction to Queuing Theory:Queuing theory is a branch of operations research because the results we obtained can be used to take business decisions. This is the mathematical study of queues. Queuing theory allows the mathematical analysis of several related processes, including joining the queue, waiting in the queue, and being served at the front of the queue. 'waiting. Using this theory, we measure the average waiting time in the queue or system, the expected number of waits or service receipts, and the probability of encountering the system. Queuing system is a model that contains the following structure when customers arrive and join a queue to wait for the service provided by n servers. After receiving the service, the customer leaves the system.Queuing Theory Equations: Kendall introduced a queuing notation A/B/S/K/N/Disc which can be used in the theory queues. In A/B/S/K/N/Disc, A is the arrival time distribution, B is the service time distribution, S is the number of servers, K is the system capacity, N is the population appellant and Disc is the service discipline assumed. Many times the last three members are omitted, then the notation becomes A/B/S and it is assumed as K = [oo], N = [oo] and Disc = FIFO. Queuing strategies are: * FIFO(First in First Out) - customers are served according to their order of arrival in the queue. * LIFO(Last in First Out) - the last customer to arrive in the queue is the one who is served first.* PS(Processor sharing) - customers are served equally.* SIRO (service in random order) - customers are served in one order random.* PR (priority) - clients are served based on middle of paper .. ....discussion with doctor. On average: 20 minutes per activity (exponential) and arrival per hour (Pisces) calculate the average number of patients in waiting room2.Clients arriving at the post office in 1 queue and more server arrival intensity 3 per minute (Poisson) service time 60 seconds (exponential) calculate: (I).number of servers needed to reach stable state. (ii) probability that there are no clients in the system with the calculated number of servers. (iii) average queue length with calculated number of servers.3. In an airport, planes land on a runway. On a runway, there are 30 arrivals per hour (Poisson), deterministic landing time of 90 seconds. Fuel cost $6,000 per hour, calculate: – average queue length. – average time during which the plane lands on the runway. – what is the hourly cost of fuel in case of delay in the queue?