报告题目：Controlling Excessive Delays in Service Systems with Time-Varying Demand

报告人：Yunan Liu

主持人：郭永江

时间：2015年5月19日周五下午15：00--16：00

地点：主楼1214

报告信息如下：

Controlling Excessive Delays in Service Systems with Time-Varying Demand

YunanLiu

（Department of Industrial & Systems Engineering North Carolina State University）

Abstract：

Queueing theory is a field driven by applications. But unfortunately, therestill remains a large gap between tractable theoretical studies and practicalapplications, such as call centers and health care systems, which have manyrealistic features (e.g., time-varying arrivals, customer abandonment,non-exponential distributions, and complicated network structures). In responseto the challenge, we study a general G_t/GI/s_t+GI queueing model, which has a non-stationarynon-Poisson arrival process (the G_t), non-exponential service times (the firstGI), and allows customer abandonment according to a non-exponential patiencedistribution (the +GI). To bridge the gap between mathematical tractability andmodel applicability, we develop fundamental principles and optimal controlpolicies for such a general queueing model.

Analytic formulas are developed to set the time-dependent number ofservers in order to stabilize important service-level indicators, including:mean customer delay, probability of abandonment, and tail probability of delay(TPoD). Taking the TPoD for example: for any delay target w > 0 andprobability target 0 < alpha < 1, we determine appropriate time-dependentstaffing levels (the s_t) so that the time-varying probability that the waitingtime exceeds a maximum acceptable value w is stabilized at alpha at all times.In addition, effective approximating formulas are provided for other important performancefunctions such as the probabilities of delay and abandonment, and the means ofdelay and queue length. Many-server heavy-traffic limit theorems in theefficiency-driven regime are developed to show that (i) the proposed staffingfunction achieves the goal asymptotically as the scale increases, and (ii) theproposed approximating formulas for other performance measures areasymptotically accurate as the scale increases. Extensive simulations show thatboth the staffing functions and the performance approximations are effective, evenfor smaller systems having an average of 3 servers.

Mini-bio：

Yunan Liu obtained his B.E. degree from the Electrical Engineering Departmentat Tsinghua University, M.S. and Ph.D. degrees from the Industrial Engineeringand Operations Research Department at Columbia University. Yunan Liu is currentlyan associate professor at North Carolina State University. His researchinterests include stochastic modeling, applied probability, simulation, optimalcontrol and queueing theory, with applications to customer contact centers,health care, production and transportation systems. Yunan Liu’s personalwebsite:  http://yunanliu.wordpress.ncsu.edu