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is the GI/G/m queue, which has m identical servers in parallel, unlimited waiting room, and
the first-come first-served queue discipline, with service and interarrival times coming from independent
sequences of independent and identically distributed random variables with general
distributions. The approximations depend on the general interarrival-time and service-time distributions
only through their first two moments. The main focus is on the expected waiting
time and the probability of having to wait before beginning service, but approximations are
also developed for other congestion measures, including the entire distributions of waiting time,
queue-length and number in system. These approximations are especially useful for incorporating
GI/G/m in larger models, such as queueing networks, wherein the approximations can be
components of rapid modeling tools.
Keywords: Approximation theory, Probability, Queueing theory, GI/G/m queue, First-come first
served queue discipline, Interarrival times, Service times, Approximations, Service-time distributions,
Queue length
39. Berman, O. and R.C. Larson. Determining optimal pool size of a temporary Call-In work force,
European Journal of Operations Research, 73, 1994, 55–64.
Abstract. This paper is one in a series that introduces concepts of just-in-time personnel.
Management of worker job time and assignment are in many ways analogous to inventory management.
Idle workers represent unutilized ‘inventoried’ personnel, imposing potentially large
costs on management. But a lack of workers when needed may force the use of otherwise unnecessary
overtime or other emergency procedures, creating excessive costs analogous to costs
of stockout in traditional inventory systems. A system having just-in-time personnel attempts
to meet all demands for personnel at minimum cost by sharply reducing both excess
worker inventory with its concomitant ‘paid lost time’ and underage of worker inventory with
its associated costs of stockout. The model in this paper focuses on one important component
of a just-in-time or ‘jit’ personnel system: response to day-to-day fluctuations in workload,
worker outages due to sick leave, personal constraints or other unscheduled events. To maximize
utilization of the JIT concept, we assume there exists a pool of call-in personnel who can
be called on the day that they are needed. Each such call-in ‘temp’ is guaranteed a minimum
number of offered days per month. A temp is paid each month for the days actually worked
plus the differential, if any, between the number of days offered and the number of days guaranteed.
Temps, like regular workers, may be unavailable on any given day due to illness, etc. The
analysis leads to an exact probabilistic model that can be solved to find the optimal pool size of
temps. Numerical results are included.
Keywords: Work force management, Optimal pool size, Temporary work force
40. Gordon, J.J. and M.S. Fowler. Accurate force and answer consistency algorithms for operator
services. Proceedings of the 14th International Teletraffic Congress, ITC-14, Elsevier, Amsterdam,
The Netherlands, 1994, 339–348.
Abstract. Operator services are big business. In the United States operator salaries per annum
amount to approximately one billion dollars. Service providers constantly strive to cut costs
while maintaining customer satisfaction. Queueing theory provides two tools to help them do
this: force algorithms for accurately provisioning their teams, and answer consistency algorithms
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