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Partial Flexibility in Routeing and Scheduling

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  04 January 2016

Osman T. Akgun ,
Rhonda Righter  and
Ronald Wolff
Osman T. Akgun*
Affiliation:
University of California, Berkeley
Rhonda Righter*
Affiliation:
University of California, Berkeley
Ronald Wolff*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, 4141 Etcheverry Hall, Berkeley, CA 94720, USA.
∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, 4141 Etcheverry Hall, Berkeley, CA 94720, USA.
∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, 4141 Etcheverry Hall, Berkeley, CA 94720, USA.
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Abstract

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We consider partial customer flexibility in service systems under two different designs. In the first design, flexible customers have their own queue and each server has its own queue of dedicated customers. Under this model, the problem is a scheduling problem and we show under various settings that the dedicated customers first (DCF) policy is optimal. In the second design, flexible customers are not queued separately and must be routed to one of the server's dedicated queues upon arrival. We extend earlier results about the ‘join the smallest work (JSW)’ policy to systems with dedicated as well as flexible arrivals. We compare these models to a routeing model in which only the queue length is available in terms of both efficiency and fairness and argue that the overall best approach for call centers is JSW routeing. We also discuss how this can be implemented in call centers even when work is unknown.

Keywords

JSWschedulingworkload routeingmajorizationsample path analysis

MSC classification

Primary: 90B22: Queues and service
Secondary: 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 3 , September 2013 , pp. 673 - 691
Copyright
© Applied Probability Trust 

References

Aalto, S., Ayesta, U. and Righter, R. (2009). On the Gittins index in the M/G/1 queue. Queueing Systems 63, 437–458.CrossRefGoogle Scholar
Ahn, H.-S., Duenyas, I. and Zhang, R. Q. (2004). Optimal control of a flexible server. Adv. Appl. Prob. 36, 139–170.Google Scholar
Akgun, O. T., Righter, R. and Wolff, R. (2011). Multiple-server system with flexible arrivals. Adv. Appl. Prob. 43, 985–1004.Google Scholar
Aksin, Z., Armony, M. and Mehrotra, V. (2007). The modern call-center: A multi-disciplinary perspective on operations management research. Prod. Operat. Manag. 16, 665–688.CrossRefGoogle Scholar
Bambos, N. and Michailidis, G. (2002). On parallel queueing with random server connectivity and routing constraints. Prob. Eng. Inf. Sci. 16, 185–203.CrossRefGoogle Scholar
Bell, S. L. and Williams, R. J. (2001). Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: asymptotic optimality of a threshold policy. Ann. Appl. Prob. 11, 608–649.Google Scholar
Daley, D. J. (1987). Certain optimality properties of the first-come first-served discipline for G/G/s queues. Stoch. Process. Appl. 25, 301–308.CrossRefGoogle Scholar
Down, D. G. and Lewis, M. E. (2010). The N-network model with upgrades. Prob. Eng. Inf. Sci. 24, 171–200.CrossRefGoogle Scholar
Ephremides, A., Varaiya, P. and Walrand, J. (1980). A simple dynamic routing problem. IEEE Trans. Automatic Control 25, 690–693.CrossRefGoogle Scholar
Foley, R. D. and McDonald, D. R. (2001). Join the shortest queue: stability and exact asymptotics. Ann. Appl. Prob. 11, 569–607.Google Scholar
Foss, S. G. (1980). Approximation of multichannel queueing systems. Siberian Math. J. 21, 851–857.Google Scholar
Gans, N., Koole, G. and Mandelbaum, A. (2003). Telephone call centers: Tutorial, review and research prospects. Manufact. Service Operat. Manag. 5, 79–141.Google Scholar
Garnett, O. and Mandelbaum, A. (2000). An introduction to skills-based routing and its operational complexities. Teaching note, Technion, Haifa, Israel.Google Scholar
Gurumurthi, S. and Benjaafar, S. (2004). Modeling and analysis of flexible queuing systems. Naval Res. Logistics 51, 755–782.Google Scholar
Harchol-Balter, M., Crovella, M. E. and Murta, C. D. (1999). On choosing a task assignment policy for a distributed server system. J. Paral. Distr. Comput. 59, 204–228.CrossRefGoogle Scholar
Harrison, J. M. (1998). Heavy traffic analysis of a system with parallel servers: asymptotic optimality of discrete-review policies. Ann. Appl. Prob. 8, 822–848.Google Scholar
Harrison, J. M. and López, M. J. (1999). Heavy traffic resource pooling in parallel-server systems. Queueing Systems 33, 339–368.Google Scholar
Hordijk, A. and Koole, G. (1990). On the optimality of the generalized shortest queue policy. Prob. Eng. Inf. Sci. 4, 477–487.Google Scholar
Hytia, E., Aaalto, S., Penttinen, A. and Virtamo, J. (2012). On the value function of the M/G/1 FIFO and LIFO queues. Submitted.Google Scholar
Johri, P. K. (1989). Optimality of the shortest line discipline with state-dependent service times. Europ. J. Operat. Res. 41, 157–161.CrossRefGoogle Scholar
Koole, G. (1992). On the optimality of FCFS for networks of multi-server queues. Tech. Rep. BS-R923, CWI, Amsterdam.Google Scholar
Koole, G. (1992). Stochastic scheduling and dynamic programming. , Leiden University.Google Scholar
Koole, G., Sparaggis, P. D. and Towsley, D. (1999). Minimising response times and queue lengths in systems of parallel queues. J. Appl. Prob. 36, 1185–1193.Google Scholar
Liu, Z. and Righter, R. (1998). Optimal load balancing on distributed homogeneous unreliable processors. Operat. Res. 46, 563–573.CrossRefGoogle Scholar
Liu, Z. and Towsley, D. (1994). Optimality of the round-robin routing policy. J. Appl. Prob. 31, 466–475.CrossRefGoogle Scholar
Liu, Z., Nain, P. and Towsley, D. (1995). Sample path methods in the control of queues. Queueing Systems 21, 293–335.Google Scholar
Mandelbaum, A. and Stolyar, A. L. (2004). Scheduling flexible servers with convex delay costs: heavy-traffic optimality of the generalized cμ-rule. Operat. Res. 52, 836–855.CrossRefGoogle Scholar
Marshall, A. W. and Olkin, I. (1979). Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.Google Scholar
Menich, R. and Serfozo, R. F. (1991). Optimality of routing and servicing in dependent parallel processing stations. Queueing Systems 9, 403–418.CrossRefGoogle Scholar
Movaghar, A. (2005). Optimal control of parallel queues with impatient customers. Performance Evaluation 60, 327–343.CrossRefGoogle Scholar
Righter, R. and Shanthikumar, J. G. (1989). Scheduling multiclass single server queueing systems to stochastically maximize the number of successful departures. Prob. Eng. Inf. Sci. 3, 323–333.Google Scholar
Saghafian, S., Van Oyen, M. P. and Kolfal, B. (2010). The “W” network and the dynamic control of unreliable flexible servers. IIE Trans. 43, 893–907.Google Scholar
Shaked, M. and Shanthikumar, G. J. (1994). Stochastic Orders and Their Applications. Academic Press, Boston, MA.Google Scholar
Sparaggis, P. D. and Towsley, D. (1994). Optimal routing and scheduling of customers with deadlines. Prob. Eng. Inf. Sci. 8, 33–49.Google Scholar
Sparaggis, P. D., Towsley, D. and Cassandras, C. G. (1993). Extremal properties of the shortest/longest nonfull queue policies in finite-capacity systems with state-dependent service rates. J. Appl. Prob. 30, 223–236.Google Scholar
Stoyan, D. (1976). A critical remark on a system approximation in queueing theory. Math. Operationsforsch. Statist. 7, 953–956.Google Scholar
Towsley, D., Sparaggis, P. D. and Cassandras, C. G. (1990). Stochastic ordering properties and optimal routing control for a class of finite capacity queueing systems. In Proc. 29th IEEE Conf. Decision and Control, pp. 658–663.CrossRefGoogle Scholar
Weber, R. R. (1978). On the optimal assignment of customers to parallel servers. J. Appl. Prob. 15, 406–413.CrossRefGoogle Scholar
Winston, W. (1977). Optimality of the shortest line discipline. J. Appl. Prob. 14, 181–189.Google Scholar
Wolff, R. W. (1977). An upper bound for multichannel queues. J. Appl. Prob. 14, 884–888.Google Scholar
Wolff, R. W. (1987). Upper bounds on work in system for multi-channel queues. J. Appl. Prob. 24, 547–551.Google Scholar
Wolff, R. W. (1989). Stochastic Modeling and Theory of Queues. Prentice Hall, Englewood Cliffs, NJ.Google Scholar