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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

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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