STA201H1 Lecture Notes - Lecture 6: Queueing Theory, Capacity Utilization, Exponential Distribution

• School: UTSG
• Department: Statistical Sciences
• Course: STA201H1
• Professor: Jeffrey Rosenthal

Document Summary

Pk (pollaczek-khinchin) formula: (cid:3118)(cid:2869) (cid:3118)+(cid:3118)(cid:2870: : average queue length, : average utilization = average throughput / average capacity = (cid:585)/(cid:586, : coefficient of variation of inter-arrival time = {a}/e{a, : coefficient of variation of service times = {s}/e{s} I = (cid:585) t: waiting time: =/(cid:585, queued units: =(cid:585, serviced units: =(cid:585)=(cid:585)/(cid:586, whole system: i=(cid:585)t=+=+=(cid:585)(+)=(cid:585)(cid:4666)+(cid:883)/(cid:586)(cid:4667, time in system: t=i(cid:2971)=+(cid:883)/(cid:586, buffer inventory = throughput rate x waiting time, total inventory = throughput rate x flow time. Om triangle example: webers hamburger on highway 11. Its strategic (business) objective: consideration of the relative costs of capacity, info, and inventory (npv, cost- In systems (cid:449)ith u(cid:374)p(cid:396)edi(cid:272)ta(cid:271)le (cid:448)a(cid:396)ia(cid:271)ilit(cid:455), a(cid:448)e(cid:396)ages do(cid:374)(cid:859)t tell the (cid:449)hole sto(cid:396)(cid:455: variability can cause loss of throughput rate. Inventory buffers or increased capacity may be needed to deal with variability. In variable systems, inventory and flow time increase non-linearly with utilization (pk formula) How to select a probability distribution: suppose you start a service business.