Sensitivity results in open, closed and mixed product form queueing networks

General formulas are proposed to quantify the effects of changing the model parameters in the so-called BCMP network [F. Baskett et al., J. ACM 22 (2) (April 1975) 248–260]. These formulas relate the derivative of the expectation of any function of both the state and the paramaters of the network with respect to any model parameter (i.e., arrival rate, mean service demand, service rate, visit ratio, traffic intensity) to known functions of the state variables. Applications of our results to sensitivity analysis and optimization problems are given.     

Buffer and server allocation in general multi‐server queueing networks

This paper deals with the joint optimization of the number of buffers and servers, an important issue since buffers and servers represent a significant amount of investment for many companies. The joint buffer and server optimization problem (BCAP) is a non‐linear optimization problem with integer decision variables. The performance of the BCAP is evaluated by a combination of a two‐moment approximation (developed for the performance analysis of finite general‐service queues) and the generalized expansion method (a well‐known method for performance analysis of acyclic networks of finite queues). A standard non‐linear optimization package is used to optimize the BCAP for a large number of experiments. A comprehensive set of numerical results is presented. The results show that the methodology is capable of handling the trade‐off between the number of servers and buffers, yielding better throughputs than previously published studies. Also, the importance of the squared coefficient of variation of the service time is stressed, since it strongly influences the approximate optimal allocation.     

Asymptotic approximations and bottleneck analysis in product form queueing networks with large populations

Asymptotic approximations are constructed for the performance measures of product form queueing networks consisting of single server, fixed rate nodes with large populations. The approximations are constructed by applying singular perturbation methods to the recursion equations of Mean Value Analysis. Networks with a single job class are studied first to illustrate the use of perturbation techniques. The leading term in the approximation is related to bottleneck analysis, but fails to be accurate if there is more than one bottleneck node. A uniform approximation is constructed which is valid for networks with many bottleneck nodes. The accuracy of the uniform approximation is demonstrated for both small and large population sizes. Next, multiclass networks are considered. The leading term in the asymptotic approximation is again related to bottleneck analysis but fails to be valid across “switching surfaces”. Across these the bottleneck nodes of the network change as a function of the fraction of jobs in the different job classes. A boundary layer correction is constructed near the switching surfaces which provides an asymptotic connection across the switching surfaces. Numerical examples are presented to demonstrate the accuracy of the results. We illustrate the asymptotic approach on some simple networks and indicate how to treat more complicated problems.     

Approximation analysis of multi-class closed queueing maintenance networks with a parts inventory system and two-phase Coxian time distributions

We consider a maintenance network where a set of bases is supported by a replacement parts inventory system and a centrally located repair depot. The ordering policy for the parts is the (S, Q) inventory policy. We extended the previous results to the network, where processing times at each node follow a two-phase Coxian distribution. The proposed network was modeled as a multi-class closed queueing network with a synchronization station. To make the analysis of the network computationally tractable, we developed a two-phase approximation method. In the first phase of the method, the proposed network was analyzed with the previous algorithm based on a product-form approximation. In the second phase, a sub-network was again analyzed with the procedure of a product-form approximation method such that the state space of the sub-network was reduced. In the analysis of a sub-network, a recursive method was also used to solve balance equations by exploiting the special structure of the Markov chain. The new algorithm provided a good estimation of the performance measures of interest. In addition to being accurate, the new algorithm is simple and converges rapidly.     

Knowledge networks in new product development projects: A transactive memory perspective

Even though an individual's knowledge network is known to contribute to the effectiveness and efficiency of his or her work in groups, the way that network building occurs has not been carefully investigated. In our study, activities of new product development teams were analyzed to determine the antecedents and consequences on the transactive memory systems, the moderating affect of task complexity was also considered. We examined 69 new product development projects and found that team stability, team member familiarity, and interpersonal trust had a positive impact on the transactive memory system and also had a positive influence on team learning, speed-to-market, and new product success. Further, we found that the impact of the transactive memory system on team learning, speed-to-market, and new product success was higher when there was a higher task complexity. Theoretical and managerial implications of the study findings are discussed.