Queue lengths in the GI(X)/M(R)/infinity service system

Service systems with queueing often have both batch arrivals and batch services. This paper focuses on the number of busy servers and waiting customers in the GI(X)/M(R)/infinity system. For the number of busy servers, we obtain a recursive relation for the partial binomial moments in terms of matrices and explicit expressions for the marginal binomial moments. Special cases are also discussed to provide a more heuristic understanding of the model

Microstructural refinement of a cast hypereutectic Al-30Si alloy by friction stir processing

Hypereutectic Al-30 wt.% Si alloy was subjected to friction stir processing (FSP) to modify the cast microstructure. FSP reduces the size of undesirable coarse silicon particles, eliminates porosities, and homogenizes and refines the cast microstructure. This paper demonstrates the effect of two pass overlap friction stir processing on microstructural refinement of Al-30Si alloy, which delineates significant reduction in size and aspect ratio of silicon particles from average 200 to 2 mu m and 4.93 to 1.75 mu m respectively. The stir zone of two pass overlap FSP exhibits relatively homogeneous Si particle distribution. Increase in frequency of silicon particles less than 1 mu m was also observed in two pass FSP stir zones. Hardness in stir zones was measured to be 75 Hv after first pass and the same changed to 85 Hv respectively after second pass. Further uniform microhardness was observed in the FSP stir zone which was not the case in as-cast Al-30Si microstructure. (C) 200

A queuing approach for inventory planning with batch ordering in multi-echelon supply chains

Order batching, Queuing systems, Inventory optimization, Multi-echelon,