# Queuing Tamagoya Food House

**Topics:**Poisson distribution, Arithmetic mean, Queueing theory

**Pages:**10 (1117 words)

**Published:**October 6, 2012

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...

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