Question

6. Consider a queueing system having two servers and no queue. There are two types of...

6. Consider a queueing system having two servers and no queue. There are two types of customers. Type 1 customers arrive according to a Poisson process having rate ??, and will enter the system if either server is free. The service time of a type 1 customer is exponential with rate ??. Type 2 customers arrive according to a Poisson process having rate ??. A type 2 customer requires the simultaneous use of both servers; hence, a type 2 arrival will only enter the system if both servers are free. The time that it takes (the two servers) to serve a type 2 customer is exponential with rate ??. Once a service is completed on a customer, that customer departs the system.
(a) Define states to analyze the preceding model.
(b) Give the balance equations.
7. In terms of the solution of the balance equations, find
(a) the average amount of time an entering customer spends in the system;
(b) the fraction of served customers that are type 1.

Homework Answers

Answer #1

6.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Customers arrive at a two-server system according to a Poisson process having rate λ = 5....
Customers arrive at a two-server system according to a Poisson process having rate λ = 5. An arrival finding server 1 free will begin service with that server. An arrival finding server 1 busy and server 2 free will enter service with server 2. An arrival finding both servers busy goes away. Once a customer is served by either server, he departs the system. The service times at server i are exponential with rates µi, where µ1 = 4, µ2...
Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential...
Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential rates μ1 and μ2, with μ1 > μ2. If server 1 becomes idle, then the customer being served by server 2 switches to server 1. a) Identify a condition on λ,μ1,μ2 for this system to be stable, i.e., the queue does not grow indefinitely long. b) Under that condition, and the long-run proportion of time that server 2 is busy.
Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential...
Consider a two-server queue with Exponential arrival rate λ. Suppose servers 1 and 2 have exponential rates μ1 and μ2, with μ1 > μ2. If server 1 becomes idle, then the customer being served by server 2 switches to server 1. condition on λ,μ1,μ2 for this system to be stable is λ< μ1+μ2 question. Under that condition, and the long-run proportion of time that server 2 is busy.
Customers arrive to a single server system in accordance with a Poisson pro- cess with rate...
Customers arrive to a single server system in accordance with a Poisson pro- cess with rate λ. Arrivals only enter if the server is free. Each customer is either a type 1 customer with probability p or a type 2 customer with probabil- ity 1 − p. The time it takes to serve a type i customer is exponential with rate μi , i = 1, 2. Find the average amount of time an entering customer spends in the system.
Customers arrive at a two server system at an exponential rate 10 customers per hour. However,...
Customers arrive at a two server system at an exponential rate 10 customers per hour. However, customers will only enter the resturant for food if there are no more than three people (including the two currently being attended to). Suppose that the amount of time required to service is exponential with a mean of five minutes for each server. (a) Write its transition diagram and balance equations. (b) What proportion of customers enter the resturant? (c) What is the average...
A simple queueing system has an arrival rate of 6 per hour and a service rate...
A simple queueing system has an arrival rate of 6 per hour and a service rate of 10 per hour. For this system the average time in line has been estimated to be 20 minutes. Using Little’s Law estimate the following: Average time in the queueing system Average number of customers in the queueing system Average number of customers in the queue Average number of customers in service.
Consider a waiting line system with the following parameters: number of servers = 4 customer arrival...
Consider a waiting line system with the following parameters: number of servers = 4 customer arrival rate = 7 per minute customer service rate (per server) = 2 per minute coefficient of variation of interarrival times = 0.8 coefficient of variation of service times = 0.6 Find the expected length of the waiting line. (Do not assume Poisson arrivals and exponential service times). (Provide two significant digits to the right of the decimal point)
Consider an M / M / 1 queueing system with capacity N = 2. Suppose that...
Consider an M / M / 1 queueing system with capacity N = 2. Suppose that customers arrive at the rate of λ per hour and are served at the rate of 8 per hour. a. What should the arrival rate be so that an arriving potential customer has a 50% chance of joining the queue? b. With λ chosen to satisfy the requirement of part a, what percentage of the customers who actually enter the system get served immediately?
(4) In a shop there are two cashiers (A and B) with a single queue for...
(4) In a shop there are two cashiers (A and B) with a single queue for them. Customers arrive at the queue as a Poisson process with rate λ, and wait for the first available cashier. If both cashiers are available, they pick one equally likely. Each cashier finishes with a customer after an exponential waiting time, with parameters µa and µb for cashier A and B, respectively. Assume that λ < µa+µb. (a) Formulate a Markov chain model with...
Customers arrive at a common queue at the coffee station with two identical coffee machines in...
Customers arrive at a common queue at the coffee station with two identical coffee machines in a busy mall at the rate of 48 per hour, following Poisson distribution. Each customer mixes his or her specialty coffee taking 2 minutes on an average following an exponential process. What is the expected number of customers in the system at this coffee station? please show work!
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT