PROBABILITY DENSITY FUNCTION OF M/G/1 QUEUES UNDER (0,K) CONTROL POLICIES: A SPECIAL CASE

In this paper we present probability density function of vacation period of M/G/1 queueing process that operates under (0,k) vacation policy, wherein the server goes on the vacation when the system becomes empty and re-opens for service immediately at the arrival of the kth customer. The number of lattice paths when last arrival is an arrival has also been derived. The transient analysis is based on approximating the general service time distribution by Coxian two-phase distribution and representing the corresponding queueing process as a lattice path. Finally the lattice path combinatorics is used to present the number of lattice paths

The measurement of retail store market share : a preliminary model

Determining individual brand and total market share is a relatively simple task that is regularly undertaken by management. However, the calculation ofretail store market share is a far more arduous task. This complexity combined with the dearth of research in the area, underlines the need for a practical but robust way of measuring store market share. The existing literature on determining market share and more specifically store market share is reviewed and a relatively simple mathematical model is proposed. The benefits of such a model in retailing management are also discussed.peer-reviewe

Total Idle Time Density Function of M/C<inf>2</inf>/1 Systems under (0,k) Policy

© Published under licence by IOP Publishing Ltd. The aim of this paper is to derive the probability density function (pdf) of the total idle time of busy period of M/C2/1 queues operating under control policies through lattice path combinatorics (LPC) approach. The service distribution is approximated by Coxian two-phase distribution. We focus on deriving the pdf of total idle time of M/C2/1 queues under (0,k) control policy, wherein the server goes on the vacation when the system becomes empty and re-opens for service immediately at the arrival of the kthcostumer. We present an important result which is the theorem of the pdf of total idle time when system is in busy period that ends with a departure