Ambulance always returns home with each service; standard M/G/1 applies a But suppose we have an emergency repair vehicle that travels directly from one customer to the next?

Single Tree center problem G is a tree. e i=1. 2..m are the end vertices

There Are Three Things Important When Buying a House: Location Location Location

Birth-and-Death Queuing Systems 1. m parallel, identical servers. 2. Infinite queue capacity. 3. Whenever users are in system (in queue plus in service) arrivals are Poisson at rate of an per unit of time. 4. Whenever n users are in system, service completions are Poisson at rate of un per unit of time. 5. FCFS discipline

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