管理科学13-排队论(等候理论).ppt

Chapter 13 - Queuing Analysis Metro Quick Lube single bay service; space for one vehicle in service and three waiting for service; mean time between arrivals of customers is 3 minutes; mean service time is 2 minutes; both inter-arrival times and service times are exponentially distributed; maximum number of vehicles in the system equals 4. Operating characteristics for ? = 20, ? = 30, M = 4: Finite Queue Length Example (1 of 2) Average queue lengths and waiting times: Finite Queue Length Example (2 of 2) Exhibit 13.6 Finite Queue Model Example Solution with Excel Exhibit 13.7 Finite Queue Model Example Solution with QM for Windows In a finite calling population there is a limited number of potential customers that can call on the system. Operating characteristics for system with Poisson arrival and exponential service times: Finite Calling Population Wheelco Manufacturing Company; 20 machines; each machine operates an average of 200 hours before breaking down; average time to repair is 3.6 hours; breakdown rate is Poisson distributed, service time is exponentially distributed. Is repair staff sufficient? ? = 1/200 hour = .005 per hour ? = 1/3.6 hour = .2778 per hour N = 20 machines Finite Calling Population Example (1 of 2) System seems inadequate. Finite Calling Population Example (2 of 2) Exhibit 13.8 Finite Calling Population Example Solution with Excel and Excel QM (1 of 2) Exhibit 13.9 Finite Calling Population Example Solution with Excel and Excel QM (2 of 2) Exhibit 13.10 Finite Calling Population Example Solution with QM for Windows In multiple-server models, two or more independent servers in parallel serve a single waiting line. Biggs Department Store service department; first-come, first-served basis. Multiple-Server Waiting Line (1 of 2) Figure 13.3 Customer Service Queuing System Multiple-Server Waiting Line (2 of 2) Multiple-Server Waiting Line Queuing Formulas (1 of 3) Assumptions: First-come first-served queue discipline Poisson a