Variability functions for parametric-decomposition approximations of queueing networks

Article Abstract:

The parametric-decomposition method is applied to estimate the steady-state performance measures of open queueing networks characterized by their non-Poisson processes and nonexponential service-time distributions. A proposal is made to improve this approach by replacing variability parameters with variability functions, which are squared coefficients of variation (SCV) of interarrival times in renewal-process approximations. The SCV in this instance is characterized as a function of the traffic intensity rho in a succeeding single-server queue. The variability functions reflect the varying levels of variability in different time scales for arrival processes that are not renewal processes. They also help explain the long-range effects in queuing networks that cannot be accounted for by variability parameters.

Approximation theory, Approximation

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Server staffing to meet time-varying demand

Article Abstract:

The operator staffing problem is examined in the context of the G(sub t)/GI(sub t)/s(sub t) queueing model. This problem involves a nonstationary stochastic service system served by a number of servers assumed to be assigned as a function of time based on projected loads. The server assignment cannot be modified adaptively in real time in accordance with the observed workload. A procedure is developed for estimating the number of servers that are needed, s(t), as a function of time t, to serve the service system. The approximate method is based on time-dependent normal distribution, with the mean and variance determined by infinite-server approximations. This approximation is compared with the exact numerical solution of the Markovian M(sub t)/M/s(sub t) model and found to be effective.

Scheduling (Management), Stochastic processes

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Predicting queuing delays

Article Abstract:

Service-oriented companies that are seeking to enhance the accuracy of predicting queueing delays may be able to do so, given the number of customers ahead of the designated customer and other related information. Waiting-time distribution functions allow companies to determine the arrival time of customers, thereby offering means to enhance customer satisfaction. The approach may also be used to improve the efficiency of customer service systems, particularly in assessing the viability of additional service agents. For nonexponential service operations, the waiting-time distribution approach may also be utilized to identify the elapsed service times of customers. This approach is highly recommended for companies that adopt the first-come, first-serve policy.

Customer Relations, Management, Customer service, Telecommunications traffic, Communications traffic

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