Application of queuing theory to washu dining
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APPLICATION OF QUEUING THEORY TO WASHU DINING. Presented by: Rohit Ray and Antonia Ferguson. INTRODUCTION. Village Dining Area 5 food areas Grill Stir fry Specialty Salad/Deli Grocery One or two cash registers open. IS THE CHECKOUT METHOD THE MOST EFFICIENT?.

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APPLICATION OF QUEUING THEORY TO WASHU DINING

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Application of queuing theory to washu dining

APPLICATION OF QUEUING THEORY TO WASHU DINING

Presented by: Rohit Ray and Antonia Ferguson


Introduction

INTRODUCTION

  • Village Dining Area

  • 5 food areas

    • Grill

    • Stir fry

    • Specialty

    • Salad/Deli

    • Grocery

  • One or two cash registers open


Is the checkout method the most efficient

IS THE CHECKOUT METHOD THE MOST EFFICIENT?

  • Should both cash registers be open?

  • Would it be more efficient for there be cash registers at each food station?


Queuing theory

QUEUING THEORY

  • Agner Krarup Erlang

    • Published first paper on queuing theory in 1909

  • Mathematical study of wait lines

  • Allows for mathematical analysis of several related processes

    • Arrival

    • Weighting in line

    • Being served

  • Calculates

    • Average weight time in line

    • Number of people in line

    • Probability waiting a certain time to be served


Queuing theory continued

Queuing Theory Continued

  • Many applications to everyday life

  • McDonalds vs. Taco Bell

  • Has been used to reduce time in:

    • Hospital wait rooms

    • Airports

    • Supermarkets

    • Printing queue


Poisson distribution

POISSON DISTRIBUTION

Poisson Distribution Equation:

  • Queuing Theory is a Poisson distribution

  • Continuous limit of the discrete binomial distribution

  • Four requirements

    • ability to divide the time interval into subintervals

    • Probability of occurrence remains constant throughout interval

    • Probability of the same occurrence in a subinterval is small enough to be discarded

    • Occurrences are independent


Poisson continued

POISSON CONTINUED

  • For one cashier the probability is 1/λ

  • Two cashiers 1/2λ


Our process

OUR PROCESS

  • Determine the probability of a customer choosing a station

  • Determine the food preparation time

  • Determine the average number of people entering the Village Dining area

  • MATLAB


One open cash register

One Open Cash Register

ave_service_time = 0.8736

ave_wait_time = 19.4549

ave_total_time =19.9618


Two cash registers open

Two Cash Registers Open

ave_service_time =0.7215

ave_wait_time =11.9748

ave_total_time =12.3420


Cash register at each station

Cash Register at Each Station

ave_service_time = 0.8599

ave_wait_time = 21.2689

ave_total_time =21.8126


Conclusion

Conclusion

  • Two cash registers are faster than one

  • Cash registers at each station cause longer waiting times

  • The wait could be shorter with a queue line


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