Markovian inventory model with two parallel queues, jockeying and impatient customers
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: Markovian inventory model with two parallel queues, jockeying and impatient customers
Markovian inventory model with two parallel queues, jockeying and impatient customers
Yugoslav Journal of Operations Research26 (2016), Number 4,467-506DOI: 10.2298/YJOR150326018JMARKOVIAN INVENTORY MODEL WITH TWO PARALLEL QUEUES, JOCKE Markovian inventory model with two parallel queues, jockeying and impatient customersEYING AND IMPATIENT CUSTOMERSK.JEGANATHANRamanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India. jegan.nathan85@yahoo.comJ. SUMATHIRamanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India.sumathijayaraman.20@gnuil.comG. MAHALAKS Markovian inventory model with two parallel queues, jockeying and impatient customersHMIRamanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India.nuthasaraswathi.g@gmail.comReceived: March 2015 / AccepMarkovian inventory model with two parallel queues, jockeying and impatient customers
ted: July 2015Abstract: Ihis article presents a perishable stochastic inventory system under continuous review at a sen-ice facility consisting of twoYugoslav Journal of Operations Research26 (2016), Number 4,467-506DOI: 10.2298/YJOR150326018JMARKOVIAN INVENTORY MODEL WITH TWO PARALLEL QUEUES, JOCKE Markovian inventory model with two parallel queues, jockeying and impatient customersize L. rhe inventory is replenished according to an (s,S) inventory policy and the replenishing times are assumed to be exponentially distributed, rhe individual customer is issued a demanded item after a random service time, which is distributed as negative exponential. The life time of each item i Markovian inventory model with two parallel queues, jockeying and impatient customerss assumed to be exponential. Customers arrive according to a Poisson process and on arrival; they join the shortest feasible queue. Moreover, if the iMarkovian inventory model with two parallel queues, jockeying and impatient customers
nventory level is more than one and one queue is empty while in the other queue, more than one customer are waiting, then the customer who has to be rYugoslav Journal of Operations Research26 (2016), Number 4,467-506DOI: 10.2298/YJOR150326018JMARKOVIAN INVENTORY MODEL WITH TWO PARALLEL QUEUES, JOCKE Markovian inventory model with two parallel queues, jockeying and impatient customersers are waiting in the other queue, rhe waiting customer independentlyreneges the system after an exponentially distributed amount of time. The joint probability distribution of the inventory level, the number OÍ customers in both queues, and the status of the server are obtained in the steady state Markovian inventory model with two parallel queues, jockeying and impatient customers. Some important system performance measures in the steady stale are derived, so as live long-run total expected cost rate.Keywords: Markov pnxess, CoMarkovian inventory model with two parallel queues, jockeying and impatient customers
ntinuous review, Inventory with service lime. Perishable commodity, Shortest queue, Jockeying and impatient.MSG 9OB22,60K25.1INTRODUCTIONResearch on qYugoslav Journal of Operations Research26 (2016), Number 4,467-506DOI: 10.2298/YJOR150326018JMARKOVIAN INVENTORY MODEL WITH TWO PARALLEL QUEUES, JOCKE Markovian inventory model with two parallel queues, jockeying and impatient customersce facility one by one and require service. In order to complete the customer service, an item from the inventor)' is needed. A served customer departs immediately from the system and the on - hand inventory decreases by one at the moment of service completion. This system is called a queueing - inv Markovian inventory model with two parallel queues, jockeying and impatient customersentory system (111. Berman and Kim 11| analyzed a queueing - inventory system with Poisson arrivals, exponential service times and zero lead times. ThMarkovian inventory model with two parallel queues, jockeying and impatient customers
e authors proved that the optimal policy is never to order when the system is empty. Berman and Sapna 151 studied queueing - inventory systems with PoYugoslav Journal of Operations Research26 (2016), Number 4,467-506DOI: 10.2298/YJOR150326018JMARKOVIAN INVENTORY MODEL WITH TWO PARALLEL QUEUES, JOCKE Markovian inventory model with two parallel queues, jockeying and impatient customersg - run expected cost rate has been obtained.Berman and Sapna |6| discussed a finite capacity system with Poisson arrivals, exponential distributed lead times and service times, rhe existence of a stationary optimal service policy has been proved. Berman and Kim [7| addressed an infinite capacity qu Markovian inventory model with two parallel queues, jockeying and impatient customerseueing - inventory system with Poisson arrivals, exponential distributed lead times and service limes, rhe authors identified a replenishment policy wMarkovian inventory model with two parallel queues, jockeying and impatient customers
hich maximized the system profit. Berman and Kim [S| studied internet based supply chains with Poisson arrivals, exponential service limes, the ErlangYugoslav Journal of Operations Research26 (2016), Number 4,467-506DOI: 10.2298/YJOR150326018JMARKOVIAN INVENTORY MODEL WITH TWO PARALLEL QUEUES, JOCKE Markovian inventory model with two parallel queues, jockeying and impatient customersy assumes the servers to be homogeneous in which the individual service rates are the same for all the servers in the system. This assumption may be valid only when the sen ice process is mechanically or electronically controlled. The multiserver queueinginventory systems with homogeneous servers ar Markovian inventory model with two parallel queues, jockeying and impatient customerse also widely studied, l or a related bibliography see |14, 151- In a queueing-inventory system with human servers, the above assumption can hardly beMarkovian inventory model with two parallel queues, jockeying and impatient customers
realized. It is common to observe server rendering service to identical jobs al different service rales. Ulis reality leads to modelling such multiseYugoslav Journal of Operations Research26 (2016), Number 4,467-506DOI: 10.2298/YJOR150326018JMARKOVIAN INVENTORY MODEL WITH TWO PARALLEL QUEUES, JOCKE Markovian inventory model with two parallel queues, jockeying and impatient customersf perishable queueing-inventory system with two heterogeneous servers including one with unreliable server and repeated attempts, theK. Jeganalhan, J. Sumathi, G. Mahalakshmi / Markovian Invenlory Model 469 first paper was by Yadavalli et.al [16| who assumed the exponential hie time for the items, e Markovian inventory model with two parallel queues, jockeying and impatient customersxponential lead lime lor the supply O1 the ordered items and exponential retrial rate for the customers in the orbit.In this paper, we consider a queuMarkovian inventory model with two parallel queues, jockeying and impatient customers
eing-inventory system consisting OÍ two parallel queues with jockeying and different server rates. The concept of jockeying is one of the important cuYugoslav Journal of Operations Research26 (2016), Number 4,467-506DOI: 10.2298/YJOR150326018JMARKOVIAN INVENTORY MODEL WITH TWO PARALLEL QUEUES, JOCKE Markovian inventory model with two parallel queues, jockeying and impatient customersg a separate and distinct queue, are available. The shortest queue problems with jockeying, but not assuming stochastic inventory management, have been widely studied by many researchers in the past. For the theory of shortest queueing problems with/ without jockeying, the often quoted articles are Markovian inventory model with two parallel queues, jockeying and impatient customersHaight [10], Zliao and Grassnum [18], Adan et.al [1, 2, 3], Cohen [9], Van lloutum et.al [13], Yaoand Knessl [17] and Tarabia 112).The rest of this paMarkovian inventory model with two parallel queues, jockeying and impatient customers
per is organized as follows. In the next section, the mathematical model and the notations used in this paper are described. Analysis of the model andYugoslav Journal of Operations Research26 (2016), Number 4,467-506DOI: 10.2298/YJOR150326018JMARKOVIAN INVENTORY MODEL WITH TWO PARALLEL QUEUES, JOCKE Markovian inventory model with two parallel queues, jockeying and impatient customerslculate the total expected cost rate, and in the section 6, we present sensitivity analysis numerically. The last section is meant for conclusion.2MODEL DESCRIPTIONIn this paper, stochastic queueing-inventory systems with the following assumptions are investigated.Consider a continuous review perish Markovian inventory model with two parallel queues, jockeying and impatient customersable inventory system with two queues in parallel and jockeying. Maximum inventory level is denoted by s and the inventory is replenished according toMarkovian inventory model with two parallel queues, jockeying and impatient customers
(s, S) ordering policy. According to this policy, the reorder level is fixed as s > 2 and an order is placed when the inventory level reaches the reoYugoslav Journal of Operations Research26 (2016), Number 4,467-506DOI: 10.2298/YJOR150326018JMARKOVIAN INVENTORY MODEL WITH TWO PARALLEL QUEUES, JOCKE Markovian inventory model with two parallel queues, jockeying and impatient customersishment. The lead time is assumed to be exponential with parameter /ỉ(> 0). The life time of the commodity is assumed to be distributed as negative exponential with parameter )'(> 0). We have assumed that an item of inventory that makes it into the service process cannot perish while in service. The Markovian inventory model with two parallel queues, jockeying and impatient customers queuing-inventory system consists 01 two parallel servers (server-1 and server-2) with different service rates Ịiỵ and fi7, respectively. The arrivalMarkovian inventory model with two parallel queues, jockeying and impatient customers
of customers is assumed to form a Poisson process with parameter A(> 0). The capacity of each queue is restricted lo L including the one being servedYugoslav Journal of Operations Research26 (2016), Number 4,467-506DOI: 10.2298/YJOR150326018JMARKOVIAN INVENTORY MODEL WITH TWO PARALLEL QUEUES, JOCKE Markovian inventory model with two parallel queues, jockeying and impatient customers 1. 1'he waiting customers receive their service one by one. The demand is for a single item per customer. The demanded item is delivered to the customer after a random time of service. The moment any server becomes idle, if the inventory level is more than one (including the servicing item) and if Markovian inventory model with two parallel queues, jockeying and impatient customersthere is a customer waiting in the other queue, the customer immediately following the customerhttps://khothuvien.cori!470 K- Jeganathan, J. Sumathi,Markovian inventory model with two parallel queues, jockeying and impatient customers
G. Mahalakshmi / Markovian Inventory Modelwho is receiving service at that counter is transferred to the idle server queue. An impatient customer leavYugoslav Journal of Operations Research26 (2016), Number 4,467-506DOI: 10.2298/YJOR150326018JMARKOVIAN INVENTORY MODEL WITH TWO PARALLEL QUEUES, JOCKE Markovian inventory model with two parallel queues, jockeying and impatient customers-1, and u2(> 0) if the customer leaves from queue-2. Note that in this model we have assumed that the servicing customer can not be impatient. Any arriving customer who finds that both queues are full is considered to be lost. Various stochastic processes involved in the system are independent of ea Markovian inventory model with two parallel queues, jockeying and impatient customersch other.2.1. Notations:e : A column vector of appropriate dimension containing all ones,0 : Zero matrix of appropriate dimension,: Entry at (Í, /)'*Markovian inventory model with two parallel queues, jockeying and impatient customers
position of a matrix A,ỗt.t. : I í ị = i'Gọi ngay
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