Exam 2 Study Guide - Lecture 11 - Variability and Waiting...

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Lecture 11 - Variability and Waiting Time -Waiting times-A "queue" is made of a server and a queue in front--Arrival time = average demand rate (# flow units/time-Capacity (#flow units/time)-We are interested in the waiting times in the queue and the queue length (inventory)-Flow time = waiting time (in queue) + activity time-Two Causes of Waiting Lines-Supply constrained process: capacity is lower than demand rate even in the absence of variability (peak hours @ Subway)-Waiting time is predicable in this case, e.g., seasonal demand-Increasing capacity-Demand constrained process: capacity is higher than demand rate but there is variability-In the arrival process: the times between the arrival of two flow units is not constant-In the service process: the time to process flow units differ from one to the other-In the presence of variability , queues can also arise if the implied utilization is bellow 100%-Arrival: Unpredicted volume swings --Random arrivals (randomness is the rule, not the exception-Incoming quality-Product mix-Activity time:-Different service request-Inherent variation-Lack of standard operating procedures-Quality (scrap / network)-Resources:-Breakdowns/maintenance-Operator absence-Set-up times-Routes-Variable routing-Dedicated machines-"No storage"! -> more vulnerable to variability-Measures of variability-Absolute measure: standard -deviation of a random variable X-Standard deviation is the most common measure of statistical dispersion , measuring how spread out the sample values of a random variable are. If the values are all close to the mean, then the standard deviation is close to zero. If many values are far from the mean, then the standard deviation is far from zero. If all the values are equal, then the standard deviation is zero-Relative measure: coefficient of variation of a random x -CV x = σ/μ- Random variables with CV < 1 are considered low-variance, while those with CV > 1 are considered high-variance.-Variability in Arrival Process-Interarrival Times-Arrival time: the time at which a customer (service request) arrives-Interarrival time: the time between two consecutive arrivals-Arrival rate: the number of arrivals per unit of time-Stationary arrival process: the expected number of customers arriving in a certain time interval is constant -Depends on the
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Exam 2 Study Guide - Lecture 11 - Variability and Waiting...

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