Project 13.1 − Internet Sales,Inc.
Internet Sales,Inc.is establishing a new ordering system to handle its on-line sales.Customers arrive randomly at an average of one every minute.On average it takes 45 seconds to process a customer's order.The current system employs one network server to process orders.This server processes orders requests one at a time in the order received.The Internet Sales,Inc. ,Analysis Team has determined that customer orders arrive according to a Poisson process and the average time spent processing an order is exponentially distributed.
Internet Sales' management knows that offering prompt,reliable on-line service is critical to their continued success.Upgrading the current on-line ordering capacity will establish their image as a "cutting edge" on-line sales company.On the other hand,too much unused capacity is inefficient and will ultimately cause company profits to decline.
Recently,the management group established a goal of serving an on-line customer immediately,90% of the time.This means that 90% of the time a customer does not have to wait to place an order on-line after using the Internet Sales,Inc.web page.A heated discussion ensued over the current system's capability of meeting this goal.
Under the current system,a customer waits if the system is busy processing another order.Network server upgrades are available in increments of $5000.Each upgrade adds the capability to process an additional order in parallel.For example if two upgrades were purchased at a cost of $10,000,orders will be processed by three independent network servers each serving at an exponential rate of one order per 45 seconds.The Analysis Team was asked to consider the alternatives and recommend a course of action to the management group.What upgrade if any)will meet the service goal set by the management group? What are the cost and performance trade-offs?

Question

Quizplus · Accepted Answer

The Answer of Project 13.1 − Internet Sales,Inc.
Internet Sales,Inc.is establishing a new ordering system to handle its on-line sales.Customers arrive randomly at an average of one every minute.On average it takes 45 seconds to process a customer's order.The current system employs one network server to process orders.This server processes orders requests one at a time in the order received.The Internet Sales,Inc. ,Analysis Team has determined that customer orders arrive according to a Poisson process and the average time spent processing an order is exponentially distributed.
Internet Sales' management knows that offering prompt,reliable on-line service is critical to their continued success.Upgrading the current on-line ordering capacity will establish their image as a "cutting edge" on-line sales company.On the other hand,too much unused capacity is inefficient and will ultimately cause company profits to decline.
Recently,the management group established a goal of serving an on-line customer immediately,90% of the time.This means that 90% of the time a customer does not have to wait to place an order on-line after using the Internet Sales,Inc.web page.A heated discussion ensued over the current system's capability of meeting this goal.
Under the current system,a customer waits if the system is busy processing another order.Network server upgrades are available in increments of $5000.Each upgrade adds the capability to process an additional order in parallel.For example if two upgrades were purchased at a cost of $10,000,orders will be processed by three independent network servers each serving at an exponential rate of one order per 45 seconds.The Analysis Team was asked to consider the alternatives and recommend a course of action to the management group.What upgrade if any)will meet the service goal set by the management group? What are the cost and performance trade-offs?