In a grocery store, there is one cashier counter. Customers arrive at the cashier counter according...

In a grocery store, there is one cashier counter. Customers arrive at the cashier counter according to a Poisson process. The arrival rate is 30 customers per hour. The service time is exponentially distributed. The mean service time is 1 minute 30 seconds.

What is the expected waiting time?

Solutions

Expert Solution

Question: In a grocery store, there is one cashier counter. Customers arrive at the cashier counter according to a Poisson process. The arrival rate is 30 customers per hour. The service time is exponentially distributed. The mean service time is 1 minute 30 seconds.

Answer:

Given that:

Arrival Time () = 30 per hour

Service Time () = 1.3 minutes = 60 / 1.3 = 46.1538461538 = 46.15 per hour (rounded**)

Now:

The expected waiting time is:

Wq = / ( - )

Therefore:

Wq = 30 / 46.15 x (46.15 - 30)

Wq = 30 / 46.15 x 16.15

Wq = 30 / 745.3225

Wq = 0.04025103227 = 0.0403 hour (or) 2.418 minutes

**Note: Since you have not provided any rounding description, i have rounded "Service Time" to two decimals for this calculation. Refer accordingly.

keosha answered 11 months ago

Next > < Previous

Related Solutions

Customers arrive to the checkout counter of a convenience store according to a Poisson process at...

Customers arrive to the checkout counter of a convenience store according to a Poisson process at a rate of two per minute. Find the mean, variance, and the probability density function of the waiting time between the opening of the counter and the following events: a. The arrival of the second customer. b. The arrival of the third customer. c. What is the probability that the third customer arrives within 6 minutes? You can use a computer if you’d like...

A small auto parts store has a single counter with one employee. Customers arrive at the counter at the rate of 10 per hour according to a Poisson distribution.

A small auto parts store has a single counter with one employee. Customers arrive at the counter at the rate of 10 per hour according to a Poisson distribution. The employee can handle 20 customers per hour and service times are exponentially distributed. Calculate (A) The probability that a customer finds an empty counter in the auto parts store (no customers waiting or being served) (B) The average number of customers waiting in the que at the auto parts store (i.e.,...

Customers arrive at a grocery store at an average of 2.2 per minute. Assume that the...

Customers arrive at a grocery store at an average of 2.2 per minute. Assume that the number of arrivals in a minute follows the Poisson distribution. Provide answers to the following to 3 decimal places. Part a) What is the probability that exactly two customers arrive in a minute? Part b) Find the probability that more than three customers arrive in a two-minute period. Part c) What is the probability that at least seven customers arrive in three minutes, given...

Customers arrive at a grocery store at an average of 2.1 per minute. Assume that the...

Customers arrive at a grocery store at an average of 2.1 per minute. Assume that the number of arrivals in a minute follows the Poisson distribution. Provide answers to the following to 3 decimal places. Part a) What is the probability that exactly two customers arrive in a minute? Part b) Find the probability that more than three customers arrive in a two-minute period. Part c) What is the probability that at least seven customers arrive in three minutes, given...

Customers arrive at a local grocery store at an average rate of 2 per minute. (a)...

Customers arrive at a local grocery store at an average rate of 2 per minute. (a) What is the chance that no customer will arrive at the store during a given two minute period? (b) Since it is a “Double Coupon” day at the store, approximately 70% of the customers coming to the store carry coupons. What is the probability that during a given two-minute period there are exactly four (4) customers with coupons and one (1) without coupons? (c)...

Q5. During peak hours, customers arrive at the cashier check-out queue in a local supermarket according...

Q5. During peak hours, customers arrive at the cashier check-out queue in a local supermarket according to a Poisson process with an average rate of 120 customers per hour. There are four cashiers serving the check-out, and they provide identical service to customers. The time to service any customer by any of the cashier is exponentially distributed with a mean of 20 seconds. If all the cashiers are busy, customers join in a single queue on arrival. (a) Compute the...

A small grocery store has a single checkout line. On Saturdays, customers arrive at the checkout...

A small grocery store has a single checkout line. On Saturdays, customers arrive at the checkout on an average of one every 8 minutes. The cashier takes an average of 6 minutes to process a single customer. We assume that the service time is randomly distributed, and the customers arrive randomly. The store's owner believes that the amount of time that a customer has to wait hurts his business; he estimates that waiting time costs him $20 per customer-hour in...

1. A grocery store counts the number of customers who arrive during an hour. The average...

1. A grocery store counts the number of customers who arrive during an hour. The average over a year is 29 customers per hour. Assume the arrival of customers follows a Poisson distribution. (It usually does.) Find the probability that at least one customer arrives in a particular one minute period. Round your answer to 3 decimals. Find the probability that at least two customers arrive in a particular 2 minute period. 2. Label each as one of the following...

Customers arrive at a department store according to a Poisson process with an average of 12...

Customers arrive at a department store according to a Poisson process with an average of 12 per hour. a. What is the probability that 3 customers arrive between 12:00pm and 12:15pm? b. What is the probability that 3 customers arrive between 12:00pm and 12:15pm and 6 customers arrive between 12:30pm and 1:00pm? c. What is the probability that 3 customers arrive between 12:00pm and 12:15pm or 6 customers arrive between 12:30pm and 1:00pm? d. What is the probability that a...

A cinema has a single ticket counter that is manned by a cashier. The cashier is...

A cinema has a single ticket counter that is manned by a cashier. The cashier is capable to handle 280 customers in an hour. Customers arrive at the counter at the rate of four customers per minute. Daniel, the owner who studied queuing models feels that all the seven assumptions for a single-channel model are met. By assuming Exponential service times and Poisson arrival rate, answer the following questions. a) State three assumptions mentioned above. b) Determine the average number...

Subjects