טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGurvich Itay
SubjectDesign and Control of the M/M/N Queue with Multi-Type
Customers and Many Servers
DepartmentDepartment of Industrial Engineering and Management
Supervisor Professor Avishai Mandelbaum


Abstract

We analyze The V-Model of Skills Based Routing. This is a model in which servers are homogeneous, and there are J customer classes having the same service requirements. With respect to the V-Model we ask the following questions:

·         Given a fixed number of servers, how to schedule servers to the different customer classes so as to optimize system performance, and

·         How many servers are required in order to minimize staffing and waiting costs while maintaining pre-specified performance goals.


We address these questions by first characterizing a scheduling scheme and staffing scheme that are asymptotically optimal as the arrival rate increases to infinity. The asymptotic optimality is in the sense that the policy (asymptotically and stochastically) minimizes the steady-state waiting and staffing costs while satisfying a pre-specified waiting probability in steady-state, asymptotically as the arrival rate grows large.


The main asymptotic framework considered in this paper is the many-server heavy-traffic regime formally introduced by Halfin and Whitt. We refer to this regime as the QED (Quality and Efficiency Driven) regime. In the concluding sections, we extend the V-Model by adding abandonment and considering optimization of staffing and control under certain cost structures. To conclude, we briefly introduce some ongoing research about the N Model of Skills Based Routing.