Lecture Outline M/M/1: finite system capacity, K M/M/m: finite system capacity, K M/M/m: finite system capacity, K=m Related observations and extensions M/E,/1 example M/G/1: epochs and transition probabilities M/G/1: derivation of L Why M/G/m, G/G/1, etc. are difficult

Lecture Outline A fundamental result for queuing networks State transition diagrams for Markovian queuing systems and networks: example Analysis of systems with dynamic demand and service rates Qualitative behavior of dynamic systems

Quiz #1: October 29 Open book, 85 minutes (start 10: 30) Chapter 4 coverage: Sections 4.1through 4.7 (inclusive); Section 4.9 (skim through 4.9.4) Review Problem Set 3 Review some old quizzes

Open book, 85 minutes(start 10: 30) Chapter 4 coverage: Sections 4.1through 4.7 (inclusive); Section 4.(skim through .9.4)[Up to lecture of 10/22] Review Problem Set 3 Review some old quizzes Prof. Barnett: Quiz review today

Countries identified as First-World are listed in the text. Some approximations attend the calculations, and the denominators are rounded off to the nearest half million. The mortality-risk difference between domestic and international flights in the first-world is not statistically significant: If major fatal crashes arise under a Poisson process at rate ) per million flights, then the observed

Air Safety: End of the Golden Age? First-World aviation has become so safe that a passenger who takes a domestic jet flight every day would on average go 36,000 years before succumbing to a fatal crash. But certain aerial dangers that were practically absent from the First World in the 1990s might be poised for a resurgence (Among these hazards are terrorism, mid-air collisions, and ground collisions. We explore recent data about the mortality risk of air travel, and discuss the prospects for the years ahead Arnold barnett

Lecture Outline Introduction to queuing systems Conceptual representation of queuing systems Codes for queuing models Terminology and notation Little's Law and basic relationships Birth-and-death processes The M/M/1 queuing system State transition diagrams Steady-state probabilities

Suppose that two aerial routes--one Eastbound and one Northbound--cross at an altitude of 35,000 feet at junction(Figure 1). In the absence of air-traffic control, the times at which eastbound planes would arrive at the junction would reflect a Poisson process with parameter(per minute)

Consider a stick of length 1. Let XI and X2 be independent random variables denoting two points n the stick at which we break the stick into three pieces. We assume that X1 and X2 are uniformly distributed over the interval

Crofton's Method Let X1 and X2 be independent random variables that are uniformly distributed over the interval [o, a]. We are interested in computing E[ -X2l]. For instance, in an urban setting, X1 and X2 may denote the location of an accident and the location where an emergency vehicle is currently parked in a road segment of length a, respectively In this case, we want to know the distance