Unit 5 2marks

UNIT 5 QUEUEING THEORYAND REPLACEMENT MODELS PART - A 1. Define a queue and a customer. Queue: The flow of customers waiting for service in a system rendering some service is called a queue. Customer: The arriving unit requires some service to be performed is called a customer. 2. What are the basic characteristics of a queuing system? (i) The input or arrival pattern (ii) The service mechanism (iii) The queue discipline (iv) The customer’s behavior 3. Define (i) Arrival pattern (ii) Service mechanism (i) Arrival pattern: This is the input pattern which describes the manner in which the customers arrive and join the queuing system since the arrival of a customer is always random; the pattern is described in terms of probability distribution. (ii) Service mechanism: The arrangement made for service by the business firm can be represented by means of probability distribution for the number of customers serviced per unit of time or the inter-service time. 4. Define queue discipline This describes the mode in which the customers select the service when the queue has been formed. The most common disciplines are (i) First come first served (ii) Last come first served (iii) Service in random order. 5. Define the following (i) Balking (ii) Reneging (iii) Priorities (iv) Jockeying (i) Balking: A customer leaves the queue because the queue is too long and the customer has no time to wait or has no sufficient space for waiting. (ii) Reneging: This happens when a customer waiting for service leaves the queue due to impatience. (iii) Priorities: In few situations, some customers are served before others regardless of their arrival. These customers have priority over others. (iv) Jockeying: Customers may switch over from one waiting line to another. This happens in a railway reservation counter. 6. What is limited and unlimited queue length? Limited queue is a situation where the waiting time is restricted to some maximum length and the unlimited queue is a situation where there are no restrictions on the maximum length of the waiting time. 7. Define transient and steady state A queuing system is said to be in transient state when its operating characteristics are dependent of time otherwise it is steady state.

8. Explain Kendall’s notation for representing queuing models. A queuing model is specified and represented symbolically in the form (a/b/c): (d/e) ; where

a – inter arrival time , b – service mechanism ,

c – number of service, d – the capacity of the system, e – queue discipline. 9. Define traffic intensity or utilization factor. A simple queue can be measured by its traffic intensity is given by  = Mean arrival rate / Mean service rate = / 10. What are the classifications of queuing models? The queuing models are classified as follows. (i) ( M/M/I) = (/FIFO) (ii) ( M/M/S) = (/FIFO) (iii) ( M/M/I) = (N/FIFO) (iv) ( M/M/S) = (N/FIFO) Where M represents Markov process indicating the number of arrivals and the completed service in the time follow poison process. The letter I & S represents a single server and multilevel respectively. The fourth letter  and N represent the capacity of the system ie infinite and finite respectively. 11. Give the formula for probability of n units in the system under single server, FCFS discipline.  = (1-  ) n where  = /  = mean arrival rate ;  = mean service rate. 12. Write the formula for finding the (i) Expected number in the queue (ii) Expected number in the non-empty queue (i) Lq = 2 / 1- where  = / (ii) Ln =  /  -  13. Write Little’s formula (i) Ls = Ws (ii) Lq = Ls - / = Wq (iii) Ws = Wq 14. Write the formula to fine the probability of waiting time more than or equal to ‘t’ in the queue  P(waiting time t) =   ( -  )  - ( -  ) wdw