Return-Path: william@bourbon.usc.edu Delivery-Date: Thu Sep 25 09:28:26 2008 X-Spam-Checker-Version: SpamAssassin 3.2.3 (2007-08-08) on merlot.usc.edu X-Spam-Level: X-Spam-Status: No, score=-2.3 required=5.0 tests=AWL,BAYES_00 autolearn=ham version=3.2.3 Received: from bourbon.usc.edu (bourbon.usc.edu [128.125.9.75]) by merlot.usc.edu (8.14.1/8.14.1) with ESMTP id m8PGSQ3G015366 for ; Thu, 25 Sep 2008 09:28:26 -0700 Received: from bourbon.usc.edu (localhost.localdomain [127.0.0.1]) by bourbon.usc.edu (8.14.2/8.14.1) with ESMTP id m8PGVY9J019915 for ; Thu, 25 Sep 2008 09:31:34 -0700 Message-Id: <200809251631.m8PGVY9J019915@bourbon.usc.edu> To: cs551@merlot.usc.edu Subject: Re: statistics doubt Date: Thu, 25 Sep 2008 09:31:34 -0700 From: Bill Cheng Someone wrote: > To calculate the the average number of customers in queue, can i use > Little's law, which is > L=lambda * average time spent in queue > > where, > lambda=average arrival rate (i.e arrival rate * customer drop probability) > average time spent in queue and the customer drop probability is being > measured by me. The lambda you are referring to is the *measured* arrival rate. So, please don't confuse it with the lambda in the spec. The measured arrival rate is the number of customers that has past through Q1 divided by the total time. Let's denote this by N/"total time". Average time spent in the queue is the total time spent in the queue for all customers divided by the total number of customers that has past through Q1. Let's denote this by "total time spent in the queue for all customers"/N. If you multiply the measured arrival rate by the average time spent in the queue, the N cancels out and you'll get "total time spent in the queue for all customers"/"total time". Well, this is exactly the same as the "area under the curve" divided by "total time". So, if you do it right, it's the same thing! -- Bill Cheng // bill.cheng@usc.edu