MAP/PH/1 queueing model with working vacation and crowdsourcing

Crowdsourcing has been used in different domains such as healthcare, computer science, environmental sciences, business and marketing. However, only recently, queueing models useful in the context of crowdsourcing have been studied. These studies involve queueing models of the type M/M/c, MAP/PH/1, and MAP/PH/c. In this paper we introduce vacation and working vacation in the context of MAP/PH/1 with crowdsourcing and highlight the qualitative aspects of the model through illustrative examples

Simulation of a Queueing Model Useful in Crowdsourcing

In this paper we study a multi-server queueing model in the context of crowdsourcing useful in service sectors. There are two types of arrivals to the system such that one group of customers after getting service from the system may serve (with a certain probability) another group. Through simulation we point out, even for a small value of this probability, the significant advantage in considering crowdsourcing by offering more traffic load (through increasing the rate of online customers without violating the stability condition) to the system resulting in more customers served (which in turn increasing the revenues when cost/profits are incorporated). Also, the role of correlation, especially a positive one, present in the inter-arrival times in the system performance measures is highlighted

Crowdsourcing and Stochastic Modeling

Crowdsourcing has been used in different domains gaining significant exposure in many fields such as healthcare, computer science, environmental sciences, business and marketing. The meaning and interpretation of crowdsourcing is varied and despite its popularity among companies in many sectors it remains little understood. However, the modeling aspects of crowdsourcing in the context of stochastic and algorithmic methods have not been considered until recently. Thus, in this expository paper we intend to provide needed connection between these two areas

M/C-2/c/K queuing model and optimization for a geriatric care center

Queuing systems with finite buffers are reasonable models for many manufacturing, telecommunication, and healthcare systems. Although some approximations exist, the exact analysis of multi-server and finite-buffer queues with general service time distribution is unknown. However, the phase-type assumption for service time is a frequently used approach. Because the Cox distribution, a kind of phase-type distribution, provides a good representation of data with great variability, it has a vast area of application in modeling service times

MAP/PH/1 queueing model with working vacation and crowdsourcing

Odwoływanie sie do madrosci tłumu (crowdsourcing-u, okazjonalnych serwisów zewnetrznych) jest wykorzystywane w róznych dziedzinach. Znane sa przykłady ze słuzby zdrowia, informatyki, nauk o srodowisku, z biznesu oraz marketingu. Jednakze dopiero od niedawna zastosowano modele teorii kolejek na uzytek modelowania tej metody powiezania zadan. Badania te obejmuja modele kolejek typu M/m/c, MAP/pH/1 i MAP/PH/c. Motywacja dla tych modeli sa usługi, których realizacje zlecamy do pewnej grupy klientów, a nastepnie ta grupa klientów decyduje sie swiadczyc podobne usługi dla innych grup klientów. Przykładowo, jedna grupa klientów odwiedza sklepy w celu zakupu penych towarów, podczas gdy drugi typ klientów zleca zakup tych dóbr przez Internet czy telefon i oczekuje ich dostarczenia. Wówczas obsługa sklepu stacjonarnego wykorzystuje odwiedzajacych ich klientówjako kurierów do obsługi inny grupy klientów. Nie wszyscy klienci sklepie sa gotowi, a w niektórych przypadkach jest to niemozliwe, aby pełnic role posredników działajacych na rzecz sklepu stacjonarnego. Wprowadzamy zatem prawdopodobienstwo tego, ze klienci jest skłonny przyjac zlecenie obsługi innych klientów. Ninieszy artykuł zajmuje sie obsługa z mozliwoscia wakacje i urlop w pracy przy modelu obsługi  MAP/PH/1 z wykorzystaniem crowdsourcingu. Zastosowano macierzowe metody analityczne do badania systemu w stanu ustalonym. Podano przykłady numeryczne wykazujace znaczace korzysci z wprowadzenia takich wariantów w klasycznych modelachkolejkowych.Crowdsourcing has been used in different domains such as healthcare, computer science, environmental sciences, business and marketing. However, only recently, queueing models useful in the context of crowdsourcing have been studied. These studies involve queueing models of the type M/M/c, MAP/PH/1, and MAP/PH/c. In this paper we introduce vacation and working vacation in the context of MAP/PH/1 with crowdsourcing and highlight the qualitative aspects of the model through illustrative examples

M/ C k / 1 Queue Model with Multiple Working Vacations

© 2016, Springer India Pvt. Ltd.In classical vacation queue models, the server completely stops serving customers during a vacation period. We deal with a system in which the server performs other supplementary jobs at a different rate rather than entirely stopping during this period. The multiple working vacation policy is considered in this study. The stationary probability distribution is obtained by using the matrix geometric method. The number of customers in the system is presented by the stochastic decomposition structure in vacation queue model. Finally, a sensitivity analysis of the model parameters on the performance measures is examined by a numerical study

Two-commodity queueing-inventory system with two classes of customers

We analyze a two-commodity queueing-inventory system with an individual ordering policy. The maximum storage capacity for the ith commodity is S-i (i = 1, 2). The reorder level for ith commodity is fixed as s(i) and whenever the inventory level of ith commodity falls on s(i) an order for Q i (= S-i - s(i)) items (i = 1, 2) is placed for that commodity irrespective of the inventory level of the other commodity. There are two types of customers, which are classified as a priority (Type-1) and ordinary (Type-2) customers. Priority customers demand only commodity-1, whereas ordinary customers demand only commodity-2. Each customer class arrives according to an independent Poisson process with different rates. Service time for each customer class is also independent of each other and follows an exponential distribution. Type-1 customers have non-preemptive priority over Type-2 customers. When the server is idle and there are both types of customers, then the service is offered to Type-1 customers. Type-2 customers have got service when there are no Type-1 customers waiting. It is assumed that waiting space for the priority customers is finite whereas there is no queue capacity for ordinary customers. The system is formulated by a five-dimensional continuous-time Markov chain. The structure of the infinitesimal generator matrix is shown to be of the QBD type. Steady-state distribution is obtained using the matrix-geometric method. The system load is formulated in a closed-form. A comprehensive numerical study is performed on the performance measures. Finally, an optimization study is presented

Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to the Poisson process and instantly destroy all items in the inventory. The arrivals of the consumer customers follow a Markovian arrival process and they can be queued in an infinite buffer. The service time of a consumer customer follows a phase-type distribution. The system receives negative customers which have Poisson flows and as soon as a negative customer comes into the system, he causes a consumer customer to leave the system, if any. One of two inventory policies is used in the systems: either (s,S) or (s,Q). If the inventory level is zero when a consumer customer arrives, then this customer is either lost (lost sale) or joins the queue (backorder sale). The system is formulated by a four-dimensional continuous-time Markov chain. Ergodicity condition for both systems is established and steady-state distribution is obtained using the matrix-geometric method. By numerical studies, the influence of the distributions of the arrival process and the service time and the system parameters on performance measures are deeply analyzed. Finally, an optimization study is presented in which the criterion is the minimization of expected total costs and the controlled parameter is warehouse capacity

A production queueing-inventory system with two-customer and a server subject to breakdown

A queueing-inventory system where the server is subject to breakdown is examined. The products in inventory are provided by production. Two different types of customers are considered. Each customer type arrives in the system according to a Poisson process with different parameters. There is only one server and the service time follows an exponential distribution. Service may be interrupted randomly due to breakdowns. There may be minor or major breakdowns and after the recovery process, the priority customer class gets service first. The described system is formulated as a level-dependent quasi-birth-death process (LDQBD). The stationarity condition is provided and the steady-state probabilities are calculated. A comprehensive numerical study is presented that examines the sensitivity of the performance measures to the change of system parameters and also investigates the optimal inventory policy according to the considered cost function