# Queuing Tamagoya Food House

Topics: Poisson distribution, Arithmetic mean, Queueing theory Pages: 10 (1117 words) Published: October 6, 2012
Queuing Theory
Most restaurants want to provide
an ideal level of service wherein they
could serve their customers at the least
minimum time. However, as the
restaurant established its name to the
public, it makes a great queuing or
waiting line that most of the customers
do not want. Not all restaurants desire
for queue since it could make
confusions to them and because of their
losses from the customers who go away
and dissatisfied. For some time, adding
chairs and tables are not enough to
solve the queuing problem.
In the case of Tamagoya Noodle
House, they have this principle of
serving the customer with their high
quality ramen regardless of the number
of customers. In short, they are more on
the quality than the quantity; not on the
profit side but rather on the quality side.
But because they really want to
serve more customers especially those
ramen lovers who came from far places,
they want to solve these queuing
problems.

Service time distribution
Arrivals
Customer 3

Customer 2

Customer 1

Service
Facility

Queue

Fig. 1 Queuing System Configuration

Assumptions of the model:
Since Tamagoya Noodle House
uses a Single-Channel, Single-Phase
model in order to avoid confusion of
customer’s order. The model we used
assumes that seven conditions exist:
1. Arrivals are served on a First-in,
First-out basis. Though some of
customers who ordered less and
or senior citizens were prioritized
to be served first.
2. Every customer waits to be
served regardless of the length of
time and so there is no balking
and reneging.
3. Arrival
of
customers
is
independent of the preceding
arrivals, but the average no. of
arrivals does not change over
time (arrival rate).
4. Arrival of customers is described
by Poisson probability distribution
and come from infinite or very
large population.
5. Service times also vary from one
customer to the next and are
independent on one another, but
their average rate is known.
6. Service times occur according to
the
negative
exponential
probability distribution.
7. The average service rate is
greater than the average arrival
rate.
With these conditions, a series of
equations can be defined using the
queue’s operating characteristics.

6. The percent idle time,
; the
probability that no one is in the
system

Queuing Equations
We let,
= mean number of arrivals per time
period (for example, per hour)
µ= mean number of people or items
served per time period
1. L= average number of customers
or units in the system

L= number in line plus the number
being served
2. W= average time
spend in the system

7. Probability that the number of
customers in the system is
greater than
:

We now apply these formulas to
the case of Tamagoya Noodle House
Calculations of the numerical
values of the preceding operating
characteristics:
Monthly Customer Counts

customers
Tue Wed Thurs Fri

Sat

Sun

1st
171 191
week
W= time spent in line plus the
time spent being served
3. The
average
number
customers in the queue,

of

4. Average time a customer spends
waiting in the queue,

5. The probability that the service is
being used:

207

360 257 246

2nd
319 173
week

191

187 314 236

3rd
215 134
week

206

237 276 329

4th
184 200
week

163

473 202 277

Tamagoya Noodle House opens
Tuesdays to Sunday at 11am to 2 pm
and 5pm to 9pm.
A. Calculation
Our team conducted the research
at lunch time. There are on the average
240 people are coming to the restaurant
in a day. The restaurant is open at 11-

2pm and 5-9pm.
From this we can
derive the arrival rate as:

customers in the restaurant is as
follows:

Table 1. Probability of More than k
Customers in the Restaurant.
We also found out from
observation
and
discussion
with
manager that each customer spends 45
minutes on average in the restaurant.
Next, we will calculate
average number of...