Queuing theory - Arrival and service process

4 important questions on Queuing theory - Arrival and service process

How is the mean service rate defined and the service rate?

(1/5)

What are the [3] assumptions in using the Kendall-Lee notation?

  1. One single line;
  2. s identical parallel servers;
  3. FCFS discipline;

Consider a three server system in which each customer's service time is governed by an exponentioal distribution. Suppose all three servers are busy and a customer is waiting. What is the probability that who is waiting will be the last of the four cutomers to complete service?

One of customers 1-3 will be th first to complete sercie. Then customer 4 will enter the service. By the no memory property customer 4's service time has the same distribution as the remaining service ties of customers 1 and 2. Thus by symmetry, customers 4, 1 and 2 will have th sesame chance of being the last customer to complete service. So (1/3)
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What does modelling a service time as an Erlang distribution with shape parameter k imply?

Implies that a customers service time may be considered to consist o a passage through k phases of service in which the time to complete each phase has the no memory property and mean of 1/k,mu

If interarrival and service times are determinisitic, each interarrival time will be exactly (1/labda) and each service time (1/mu) 

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