BA341 16th Edition Lecture 16 Outline of Last Lecture I Sequence of Decisions II In summary III Managing Process Variability Outline of Current Lecture IV Service Call Center with uncertainty V Waiting line terminology VI M M 1 Queue Current Lecture Managing Process Variability continued Consider a Service Call Center with uncertainty On average customer arrivals are 1 every 4 minutes Are there any blocked calls Are there any customers tired of waiting In a world filled with uncertainty Avg Arrival Rate 15 hr Avg Call Processing Rate 20 hr Avg Depart Rate Min Min 15 hr 20 hr 15 hr Calls on hold are in queen and sales reps answer calls are in service These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Some Performance Metrics Avg Time in Queue Wq in Service ts and in System Ws o Avg time in queue avg time in service avg time in system Avg Number of Customers Waiting Lq in Service and in System Ls Avg Utilization of Service Provider Waiting Line Terminology Arrival Characteristics o Arrival Population Infinite vs Finite o Pattern of Arrivals Independent arrivals arrival rate Queue Discipline o Rule that determines the order in which arrivals are serviced First in first out FIFO earliest due date EDD etc o Customer Behavior Wait vs Leave Service Characteristics o Single multiple channel s One multiple server s o Independent service time service rate M M 1 Queue Arrival Characteristics o Arrival Population Infinite o Pattern of Arrivals Poisson distributed independent arrivals with ARRIVAL RATE Queue Discipline o First in first out FIFO Fist in first served FIFS o Customer Behavior Wait until served Service Characteristics o Single channel queuing system with one server o Independent service time with negative exponential distribution SERVICE RATE Note Waiting Line Performance Metrics for M M 1 Queue Service utilization or probability that the server is busy o arrival rate service rate o probability that the server is idle 1 Number of customers in the system o Ls 1 or Ls Time in the System o Ws Ls 1 This formula is in essence Little Laws from the previous chapters WIP THt x THr Number of Customers waiting o Lq Ls 2 Waiting time o Wq Ws ts Lq o Where ts 1 Determining Performance Metrics M M 1 System 15 h 20 h The average utilization of the sales rep is o 15 20 75 The probability the sales rep is idle is o 1 1 0 75 0 25 The probability that an arriving customer finds the system empty is The same as the probability the sales rep is idle 0 25
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