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When you enter the bank, you find that there are only two tellers, both busy serving...
2. A bank has two tellers. When Taha enters the bank, both tellers are busy (serving...
2. A bank has two tellers. When Taha enters the bank, both tellers are busy (serving Ahmet and Kami. Assume that the service time of the tellers is exponentially distributed with (a) (5 points) Calculate the probability that Taha is the last person who is done with (b) (7 points) Let X and Y be the service times for Ahmet and Mehmet, respectively. independent of each other and previous customers. the teller Calculate the cumulative distribution function (CDF) of the...
Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The bank...
Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The bank lobby has enough space for 10 customers. When the lobby is full, an arriving customers goes to another branch and is lost. The bank manager assigns one teller to customer service as long as the number of customers in the lobby is 3 or less. She assigns two tellers if the number is more than 3 but less than 8. Otherwise she assigns...
2. [3] Suppose you arrive to a service system with three parallel servers. All servers are busy, ...
2. [3] Suppose you arrive to a service system with three parallel servers. All servers are busy, and there is no customer ahead of you in the queue. As soon as one of the servers is free, you will be served by that server. Service times at each server are exponentially distributed with rates 1, 2, and us. What is the expected time you will spend in the system?
2. [3] Suppose you arrive to a service system with three...
I need matlab code for solving this problem Clients arrive to a certain bank according to a Poisson Process. There is a...
I need matlab code for solving this problem
Clients arrive to a certain bank according to a Poisson Process. There is a single bank teller in the bank and serving to the clients. In that MIM/1 queieing system; clients arrive with A rate 8 clients per minute. The bank teller serves them with rate u 10 clients per minute. Simulate this queing system for 10, 100, 500, 1000 and 2000 clients. Find the mean waiting time in the queue and...
Problem 4. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive a...
Problem 4. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive ac cording to a Poisson process at a mean rate of 4 per minute. However, business is growing and management projects that the mean arrival rate will be 6 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 0.5 minute. Management has established the following guidelines for a satis- factory level...
A hair salon is run by two stylists, Darrel and Jill, each capable of serving four...
A hair salon is run by two stylists, Darrel and Jill, each capable of serving four customers per hour, on average. Six customers, on average, arrive at the salon each hour. (Assume Poisson arrivals and exponential service times) a) If all arriving customers wait in a common line for the next available stylist, how long would a customer wait in line, on average, before being served? b) Suppose that 50 percent of the customers want to be served only by...
(25 points,) Let X and Y be two independent and identically distributed random variables that have exponential distribution with rates 1 respectively. Find the distribution of Note: you can give eith...
(25 points,) Let X and Y be two independent and identically distributed random variables that have exponential distribution with rates 1 respectively. Find the distribution of Note: you can give either cdf or pdf)
(25 points,) Let X and Y be two independent and identically distributed random variables that have exponential distribution with rates 1 respectively. Find the distribution of Note: you can give either cdf or pdf)
C PROGRAM: In this assignment, you will use the concept of POSIX threads, semaphores and mutex...
C PROGRAM: In this assignment, you will use the concept of POSIX threads, semaphores and mutex locks. Consider a very small bank: XYZ. This bank has only one cashier (aka bank teller or customer representative) and a small waiting room for any incoming customers while the cashier is busy with other customer. There is a sofa which can only hold 5 people at maximum. The cashier can only serve one customer at any time. When the cashier is serving one...
4. When John enters the bank office, there are four customers waiting in line and one...
4. When John enters the bank office, there are four customers waiting in line and one customer is being served. There is a single clerk and the service time is exponentially distributed with λ-10 customer per hour, independent of everything else. (a) (2 points) What is the average service time per customer? (b) (4 points) What is the distribution of John's waiting time? (c) (4 points) Calculate the expected value and variance of John's waiting time. (d) (10 points) It...
A small barbershop, operated by a single barber, has room for at most two customers. Potential...
A small barbershop, operated by a single barber, has room for at most two customers. Potential customers arrive according to a Poisson process with rate three customers per hour. The successive service times are independent exponential random variables with mean 15 minutes. (a) Model this system as a CTMC. (b) What is the proportion of time the barber is busy? (c) What is the expected long-run average number of customers in the shop? (d) If the barber could work twice...
2. A bank has two tellers. When Taha enters the bank, both tellers are busy (serving Ahmet and Kami. Assume that the service time of the tellers is exponentially distributed with (a) (5 points) Calculate the probability that Taha is the last person who is done with (b) (7 points) Let X and Y be the service times for Ahmet and Mehmet, respectively. independent of each other and previous customers. the teller Calculate the cumulative distribution function (CDF) of the...
2. [3] Suppose you arrive to a service system with three parallel servers. All servers are busy, and there is no customer ahead of you in the queue. As soon as one of the servers is free, you will be served by that server. Service times at each server are exponentially distributed with rates 1, 2, and us. What is the expected time you will spend in the system?
2. [3] Suppose you arrive to a service system with three...
I need matlab code for solving this problem
Clients arrive to a certain bank according to a Poisson Process. There is a single bank teller in the bank and serving to the clients. In that MIM/1 queieing system; clients arrive with A rate 8 clients per minute. The bank teller serves them with rate u 10 clients per minute. Simulate this queing system for 10, 100, 500, 1000 and 2000 clients. Find the mean waiting time in the queue and...
Problem 4. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive ac cording to a Poisson process at a mean rate of 4 per minute. However, business is growing and management projects that the mean arrival rate will be 6 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 0.5 minute. Management has established the following guidelines for a satis- factory level...
(25 points,) Let X and Y be two independent and identically distributed random variables that have exponential distribution with rates 1 respectively. Find the distribution of Note: you can give either cdf or pdf)
(25 points,) Let X and Y be two independent and identically distributed random variables that have exponential distribution with rates 1 respectively. Find the distribution of Note: you can give either cdf or pdf)
4. When John enters the bank office, there are four customers waiting in line and one customer is being served. There is a single clerk and the service time is exponentially distributed with λ-10 customer per hour, independent of everything else. (a) (2 points) What is the average service time per customer? (b) (4 points) What is the distribution of John's waiting time? (c) (4 points) Calculate the expected value and variance of John's waiting time. (d) (10 points) It...
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