OPTIMAL UTILIZATION OF SERVICE FACILITY FOR A k-OUT-OF-n SYSTEM WITH REPAIR BY EXTENDING SERVICE TO EXTERNAL CUSTOMERS IN A RETRIAL QUEUE

In this paper, we study a k-out-of-n system with single server who provides service to external customers also. The system consists of two parts:(i) a main queue consisting of customers (failed components of the k-out-of-n system) and (ii) a pool (of finite capacity M) of external customers together with an orbit for external customers who find the pool full. An external customer who finds the pool full on arrival, joins the orbit with probability and with probability 1− leaves the system forever. An orbital customer, who finds the pool full, at an epoch of repeated attempt, returns to orbit with probability (< 1) and with probability 1 − leaves the system forever. We compute the steady state system size probability. Several performance measures are computed, numerical illustrations are provided.

Acetalization of ketones on K-10 clay and rare earth exchanged HFAU-Y zeolites: A mild and facile procedure for the synthesis of dimethylacetals

Dimethylacetals of ketones; cyclohexanone, acetophenone, and benzophenone have been prepared by reacting ketones with methanol under mild reaction conditions. Large pore zeolites (H-Y and its rare earth metal, Ce3+, La3+, and RE3+ modified forms), and mesoporous clay (K-10 montmorillonite and its cerium exchanged counterpart) with regular pore structure, silica and silica-alumina have been used as catalysts. Clay catalysts are found to be much more active than zeolites, thanks to slightly bigger pore size. The nature of the pores of the solid acid catalysts determine acetalization efficiency of a particular catalyst. As evidenced by the reaction time studies, the catalyst decay is greater over the zeolites than over the clays. Carrying out the reaction with ketones of different molecular sizes it is shown that K-10 clays and rare earth exchanged H-Y zeolites are promising environmentally friendly catalysts for their use in the production fine chemicals.