Question

Case Study: Pantry Shop (modified)

Customers arrive at the Pantry Shop store at a rate of 3 per minute and the Poisson distribution accurately defines this rate. A single cashier works at the store, and the average time to serve a customer is 15 seconds, and the exponential distribution may be used to describe the distribution of service times.

- What are λ and μ in this situation?
- Using Kendall notation, what type of queuing system is this?
- How many minutes does the average customer spend waiting in line?

Answer #1

Customers arrive at a shop at the rate of 7 per 10-minute
interval. what is the probability that we need to wait at least 10
minutes before the next customer arrives at the shop? Obtain the
probability using Poisson distribution and Exponential
distribution.

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.
1. What is the expected number of customers waiting in the
system.
2. What is the expected waiting time.( unit in minutes)
3. What is the utilization rate (unit in %) of
the cashier?

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 coffee shop at a rate of 40 per hour. There
are 2 servers available and it takes an average of 1 minute to
serve each customer.
Using Table 12-6, what is the probability of no customers in the
system?
0.333
0.5
0.667
0

A large bank branch employs 5 tellers to serve its customers.
Customers arrive according to a Poisson process at a mean rate of 3
per minute. The transaction time between the teller and customer
has an exponential distribution with a mean of 1 minute. The
management has established the following guidelines for the
satisfactory level of service to customers:
The average number of customers waiting in line to begin
service should not exceed 1.
At least 95% of the time,...

Suppose that the customers arrive at a hamburger stand at an
average rate of 49 per hour, and the arrivals follow a Poisson
distribution. Joe, the stand owner, works alone and takes an
average of 0.857 minutes to serve one customer. Assume that the
service time is exponentially distributed.
a) What is the average number of people waiting in queue and in
the system? (2 points)
b) What is the average time that a customer spends waiting in
the queue...

Suppose that the customers arrive at a hamburger stand at an
average rate of 49 per hour, and the arrivals follow a Poisson
distribution. Joe, the stand owner, works alone and takes an
average of 0.857 minutes to serve one customer. Assume that the
service time is exponentially distributed.
a) What is the average number of people waiting in queue and in
the system? (2 points)
b) What is the average time that a customer spends waiting in
the queue...

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.
What is the probability that at least seven customers arrive in
three minutes, given that exactly two arrive in the first
minute?

(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 suburban ticket outlet at the rate of 3
per hour on Monday mornings. This can be described by a Poisson
distribution. Selling the tickets and providing general information
takes an average of 10 minutes per customer, and varies
exponentially. There are 3 ticket agents on duty on Mondays. On
Average, how much time does a customer spend Waiting in Line?
Question 5 options:
.001
.167
.0005
.1837
None of the Answers Listed is Correct

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