Annals of Operations Research

He, Qi-Ming; Takine, Tetsuya; Taylor, Peter; Zhang, Hanqin

doi: 10.1007/s10479-008-0310-9pmid: N/A

Deepak, T.; Krishnamoorthy, A.; Narayanan, Viswanath; Vineetha, K.

doi: 10.1007/s10479-007-0304-zpmid: N/A

An inventory system with two parallel service facilities is considered. A certain number of customers are transferred from longer to shorter queue whenever their difference reaches a prescribed quantity. Along with this customer transfer, a certain quantity of inventory is also transferred, depending on availability. Further, if one of the queues has customers, but has no inventoried items whereas the other has at least one inventoried item to spare, then exactly one item is taken to the former and service begins thereby enhancing the efficiency of the system. Stability of the system is analysed. Several performance measures that helps in efficient design of such systems, are computed. Some numerical results are provided.

Ramaswami, V.; Woolford, Douglas; Stanford, David

doi: 10.1007/s10479-008-0309-2pmid: N/A

For applications of stochastic fluid models, such as those related to wildfire spread and containment, one wants a fast method to compute time dependent probabilities. Erlangization is an approximation method that replaces various distributions at a time t by the corresponding ones at a random time with Erlang distribution having mean t. Here, we develop an efficient version of that algorithm for various first passage time distributions of a fluid flow, exploiting recent results on fluid flows, probabilistic underpinnings, and some special structures. Some connections with a familiar Laplace transform inversion algorithm due to Jagerman are also noted up front.

Squillante, Mark; Zhang, Yanyong; Sivasubramaniam, Anand; Gautam, Natarajan

doi: 10.1007/s10479-008-0312-7pmid: N/A

This paper introduces a generalization of the classical parallel-server fork-join queueing system in which arriving customers fork into multiple tasks, every task is uniquely assigned to one of the set of single-server queues, and each task consists of multiple iterations of different stages of execution, including task vacations and communication among sibling tasks. Several classes of dynamic polices are considered for scheduling multiple tasks at each of the single-server queues to maintain effective server utilization. The paper presents an exact matrix-analytic analysis of generalized parallel-server fork-join queueing systems, for small instances of the stochastic model, and presents an approximate matrix-analytic analysis and fixed-point solution, for larger instances of the model.