compute probabilities-transitions and transition rate, Operation Research

Consider a queueing system with 1 counter, to which groups of customers arrive according to a Poisson proces with intensity l. The size of a group is 1 with probability p and 2 with probability 1-p. Customers are served one by one. The service time has exponential distribution with mean m-1 . Service times are mutually independent and independent of the arrival proces. The system may contain at most 3 customers. If the system is full upon arrival of a group, or if the system may contain only one additional customer upon arrival of a group of size 2, then all customers in the group are lost and will never return. Let Z(t) record the number of customers at time t.

(a)    Explain why {Z(t), t³0}is a Markov proces and give the diagram of transitions and transition rates.

(b)   Give the equilibrium equations (balance equations) for the stationary probabilities Pn , n=0,1,2,3.

(c)    Compute these probabilities Pn , n=0,1,2,3.

The answers to the following questions may be provided in terms of the probabilities Pn  (except for (h)).

(d)   Give an expression for the average number of waiting customers.

(e)   Give the departure rate and the rate at which customers enter the queue.

(f)    Give an expression for the average waiting time of a customer.

(g)   What is the fraction of time the counter is busy?

(h)   What is the average length of an idle period?

(i)    Determine from  (g) and (h) the average length of a period the system is occupied (= at least 1 customer in the system).

(j)    What is the rate at which groups of size 2 enter the queue?

Posted Date: 3/5/2013 8:13:44 AM | Location : United States







Related Discussions:- compute probabilities-transitions and transition rate, Assignment Help, Ask Question on compute probabilities-transitions and transition rate, Get Answer, Expert's Help, compute probabilities-transitions and transition rate Discussions

Write discussion on compute probabilities-transitions and transition rate
Your posts are moderated
Related Questions
Answering Question to Finding Shortest Path - Operation Research Assignment Help Finding answers for shortest path problems are quite interesting and not easy to solve. In solv

A company is planning its advertising strategy for the next year for its three major products.

DECILES The nine points  on the scale of observations  ( or  values of the variable) which divide the total  frequency into ten  equal parts  are called deciles for the data

Assignments should be submitted via FLO by the above deadline. Penalties for late submission are as set out in the topic SAM on FLO. Extensions can be granted in line with standard

Principles of Report Writing Reports writing  may  involve the followings principles . a. Easy to Follow : The body of the  report should  be written in a self evident and

Rank Methods Spearman s When the variables  under  consideration are  not capable  of quantitative  measurement but can  be arranged  in serial  order( ranks) we find  correla

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

Classification of documents by information Characteristics: The schemes of classification advocated by Hanson and Grogan are mainly based on the information characteristics of

Description      Skype is currently the most popular VoIP software in the world. Existing research has indicated that Skype can provide better voice/video quality in adverse net

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i