Technical Note - Queueing Systems with Synergistic Servers

We consider tandem lines with finite buffers and flexible, heterogeneous servers that are synergistic in that they work more effectively in teams than on their own. Our objective is to determine how the servers should be assigned dynamically to tasks in order to maximize the long-run average throughput. In particular, we investigate when it is better to take advantage of synergy among servers, rather than exploiting the servers' special skills, to achieve the best possible system throughput. We show that when there is no trade-off between server synergy and servers' special skills (because the servers are generalists who are equally skilled at all tasks), the optimal policy has servers working in teams of two or more at all times. Moreover, for Markovian systems with two stations and two servers, we provide a complete characterization of the optimal policy and show that, depending on how well the servers work together, the optimal policy either takes full advantage of servers' special skills, or full advantage of server synergy (and hence there is no middle ground in this case). Finally, for a class of larger Markovian systems, we provide sufficient conditions that guarantee that the optimal policy should take full advantage of server synergy at all times.

[1]  Zeynep Akşin,et al.  The Modern Call Center: A Multi‐Disciplinary Perspective on Operations Management Research , 2007 .

[2]  Wallace J. Hopp,et al.  Agile workforce evaluation: a framework for cross-training and coordination , 2004 .

[3]  U. Rieder,et al.  Markov Decision Processes , 2010 .

[4]  O. Zeynep Akşin,et al.  A REVIEW OF WORKFORCE CROSS-TRAINING IN CALL CENTERS FROM AN OPERATIONS MANAGEMENT PERSPECTIVE , 2007 .

[5]  Wallace J. Hopp,et al.  Performance Opportunity for Workforce Agility in Collaborative and Noncollaborative Work Systems , 2001 .

[6]  Cheng-Hung Wu,et al.  Dynamic allocation of reconfigurable resources ina two-stage Tandem queueing system with reliability considerations , 2006, IEEE Transactions on Automatic Control.

[7]  Izak Duenyas,et al.  Optimal stochastic scheduling of a two-stage tandem queue with parallel servers , 1999, Advances in Applied Probability.

[8]  Seyed M. R. Iravani,et al.  Optimal dynamic assignment of a flexible worker on an open production line with specialists , 2006, Eur. J. Oper. Res..

[9]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[10]  Sigrún Andradóttir,et al.  Throughput Maximization for Tandem Lines with Two Stations and Flexible Servers , 2005, Oper. Res..

[11]  E. Lerzan Örmeci,et al.  Dynamic admission control in a call center with one shared and two dedicated service facilities , 2004, IEEE Transactions on Automatic Control.

[12]  Sigrún Andradóttir,et al.  Dynamic assignment of dedicated and flexible servers in tandem lines , 2007 .

[13]  Mark E. Lewis,et al.  On the Introduction of an Agile, Temporary Workforce into a Tandem Queueing System , 2005, Queueing Syst. Theory Appl..

[14]  Rhonda Righter,et al.  Dynamic load balancing with flexible workers , 2006, Advances in Applied Probability.

[15]  John A. Buzacott,et al.  Commonalities in Reengineered Business Processes: Models and Issues , 1996 .

[16]  Sigrún Andradóttir,et al.  Server Assignment Policies for Maximizing the Steady-State Throughput of Finite Queueing Systems , 2001, Manag. Sci..

[17]  Avishai Mandelbaum,et al.  Telephone Call Centers: Tutorial, Review, and Research Prospects , 2003, Manuf. Serv. Oper. Manag..

[18]  Sigrún Andradóttir,et al.  Partial Pooling in Tandem Lines with Cooperation and Blocking , 2006, Queueing Syst. Theory Appl..