A time-varying call center design via lagrangian mechanics

Robert C. Hampshire, Otis B. Jennings, William A. Massey

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We consider a multiserver delay queue with finite additional waiting spaces and time-varying arrival rates, where the customers waiting in the buffer may abandon. These are features that arise naturally from the study of service systems such as call centers. Moreover, we assume rewards for successful service completions and cost rates for service resources. Finally, we consider service-level agreements that constrain both the fractions of callers who abandon and the ones who are blocked. Applying the theory of Lagrangian mechanics to the fluid limit of a related Markovian service network model, we obtain near-profit-optimal staffing and provisioning schedules. The nature of this solution consists of three modes of operation. A key step in deriving this solution is combining the modified offered load approximation for loss systems with our fluid model. We use them to estimate effectively both our service-level agreement metrics and the profit for the original queuing model. Second-order profit improvements are achieved through a modified offered load version of the conventional square root safety rule.

Original languageEnglish (US)
Pages (from-to)231-259
Number of pages29
JournalProbability in the Engineering and Informational Sciences
Issue number2
StatePublished - Apr 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


Dive into the research topics of 'A time-varying call center design via lagrangian mechanics'. Together they form a unique fingerprint.

Cite this