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Industrial & Manufacturing Engineering Publications

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Queueing System With Potential For Recruiting Secondary Servers, Srinivas Chakravarthy, Alexander N. Dudin, Sergey A. Dudin, Olga S. Dudina Jan 2023

Queueing System With Potential For Recruiting Secondary Servers, Srinivas Chakravarthy, Alexander N. Dudin, Sergey A. Dudin, Olga S. Dudina

Industrial & Manufacturing Engineering Publications

In this paper, we consider a single server queueing system in which the arrivals occur according to a Markovian arrival process (MAP). The served customers may be recruited (or opted from those customers’ point of view) to act as secondary servers to provide services to the waiting customers. Such customers who are recruited to be servers are referred to as secondary servers. The service times of the main as well as that of the secondary servers are assumed to be exponentially distributed possibly with different parameters. Assuming that at most there can only be one secondary server at any given …

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A Retrieval Queueing Model With Feedback, Agassi Melikov, Srinivas Chakravarthy, Sevinc Aliyeva Nov 2022

A Retrieval Queueing Model With Feedback, Agassi Melikov, Srinivas Chakravarthy, Sevinc Aliyeva

Industrial & Manufacturing Engineering Publications

A multi-server retrial queuing model with feedback is considered in this paper.Input flow of calls is modeled using a Markovian Arrival Process (M AP) and the service time is assumed to follow an exponential distribution. An arriving call enters into service should there be a free server. Otherwise, in accordance to Bernoulli trials, the call will enter into an infinite orbit (referred to as a retrial orbit) to retry along with other calls to get into service or will leave the system forever. After obtaining a service each call, independent of the others, will either enter into a finite orbit …

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Analysis Of A Queueing Model With Map Arrivals And Heterogeneous Phase-Type Group Services, Srinivas R. Chakravarthy Sep 2022

Analysis Of A Queueing Model With Map Arrivals And Heterogeneous Phase-Type Group Services, Srinivas R. Chakravarthy

Industrial & Manufacturing Engineering Publications

Queueing models have proven to be very useful in real-life applications to enable the practitioners to optimize the limited resources to conduct their businesses as well as offer services efficiently. In general, we can group such applications into two sectors: manufacturing and service. These two sectors cover everything we deal with on a day-to-day basis. Queues in which the services are offered in blocks (or groups or batches) are well established in the literature and have a wide variety of applications in practice. In this paper, we look at one such queueing model in which the arrivals occur according to …

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Queuing-Inventory Models With Map Demands And Random Replenishment Opportunities, Srinivas R. Chakravarthy, B. Madhu Rao May 2021

Queuing-Inventory Models With Map Demands And Random Replenishment Opportunities, Srinivas R. Chakravarthy, B. Madhu Rao

Industrial & Manufacturing Engineering Publications

Combining the study of queuing with inventory is very common and such systems are referred to as queuing-inventory systems in the literature. These systems occur naturally in practice and have been studied extensively in the literature. The inventory systems considered in the literature generally include (s, S)-type. However, in this paper we look at opportunistic-type inventory replenishment in which there is an independent point process that is used to model events that are called opportunistic for replenishing inventory. When an opportunity (to replenish) occurs, a probabilistic rule that depends on the inventory level is used to determine whether to avail …

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Queueing Models With Map Arrivals Useful In Service Sectors, Srinivas R. Chakravarthy Jan 2021

Queueing Models With Map Arrivals Useful In Service Sectors, Srinivas R. Chakravarthy

Industrial & Manufacturing Engineering Publications

Queueing models have found applications in many fields, notably in service sectors. In this paper, we study queueing models that have significant applications in service sectors. We look at multi-server systems with MAP arrivals. We assume phase type services for single server systems and exponential services when dealing with multi-server systems. All arriving customers finding no idle server will not wait in the system to receive services but rather leave their information in a registry list. These customers will be reached out on a first-come-first-served basis (FCFS) by an idle server soon after completing its current service. The reach out …

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A Retrial Queueing Model With Thresholds And Phase Type Retrial Times, Srinivas R. Chakravarthy May 2020

A Retrial Queueing Model With Thresholds And Phase Type Retrial Times, Srinivas R. Chakravarthy

Industrial & Manufacturing Engineering Publications

There is an extensive literature on retrial queueing models. While a majority of the literature on retrial queueing models focuses on the retrial times to be exponentially distributed (so as to keep the state space to be of a reasonable size), a few papers deal with nonexponential retrial times but with some additional restrictions such as constant retrial rate, only the customer at the head of the retrial queue will attempt to capture a free server, 2-state phase type distribution, and finite retrial orbit. Generally, the retrial queueing models are analyzed as level-dependent queues and hence one has to use …

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Queueing-Inventory Models For A Two-Vendor System With Positive Service Times, Srinivas Chakravarthy, Khizer Hayat Jan 2020

Queueing-Inventory Models For A Two-Vendor System With Positive Service Times, Srinivas Chakravarthy, Khizer Hayat

Industrial & Manufacturing Engineering Publications

Queueing-inventory systems wherein the demands are processed with random service times have been getting a lot of attention recently. In such systems, each demand needs one or more inventory items and needs positive processing times. The inventory is generally replenished using -type policy and the lead times are assumed to be random. In this paper we introduce the concept of multiple vendors who will be responsible for the replenishment of inventory. Under the assumptions of a two-vendor system wherein the demands occurring according to a Markovian arrival process, the service times to be of phase type, and the lead times …

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Bmap/G/C Queueing Model With Group Clearance Useful In Telecommunications Systems – A Simulation Approach, Srinivas Chakravarthy, Alexander Rumyantsev May 2019

Bmap/G/C Queueing Model With Group Clearance Useful In Telecommunications Systems – A Simulation Approach, Srinivas Chakravarthy, Alexander Rumyantsev

Industrial & Manufacturing Engineering Publications

Queueing models in which customers or messages arrive in batches with inter-arrival times of batches possibly correlated and services rendered in batches of varying sizes play an important role in telecommunication systems. Recently queueing models of BMAP/G/1-type in which a new type of group clearance was studied using embedded Markov renewal process as well as continuous time Markov chain whose generator has a very special structure. In this paper, we generalize these models to multi-server systems through simulation approach. After validating the simulation model for the single server case, we report our simulated results for much more general situations.

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Efficient Redundancy Techniques In Cloud And Desktop Grid Systems Using Map/G/C-Type Queues, Srinivas R. Chakravarthy, Alexander Rumyantsev Mar 2018

Efficient Redundancy Techniques In Cloud And Desktop Grid Systems Using Map/G/C-Type Queues, Srinivas R. Chakravarthy, Alexander Rumyantsev

Industrial & Manufacturing Engineering Publications

Cloud computing is continuing to prove its flexibility and versatility in helping industries and businesses as well as academia as a way of providing needed computing capacity. As an important alternative to cloud computing, desktop grids allow to utilize the idle computer resources of an enterprise/community by means of distributed computing system, providing a more secure and controllable environment with lower operational expenses. Further, both cloud computing and desktop grids are meant to optimize limited resources and at the same time to decrease the expected latency for users. The crucial parameter for optimization both in cloud computing and in desktop …

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Comparing Three Instructional Modes For An Engineering Economy Course, Farnaz Ghazi Nezami, M. B. Yildirim, G. Grossi Crema Dec 2016

Comparing Three Instructional Modes For An Engineering Economy Course, Farnaz Ghazi Nezami, M. B. Yildirim, G. Grossi Crema

Industrial & Manufacturing Engineering Publications

This study compares three instructional modes in an “Engineering Economy” course: online, face-to-face (FtF), and flipped. Engineering Economy is a core course in this study and incorporates students with diverse backgrounds from different engineering majors. To discern the relation between student characteristics and teaching modality, an online questionnaire was designed for each mode and distributed over a two-year period. Data was collected and several statistical analyses were conducted to study the relationship between pedagogical delivery modes and various student-based factors such as gender, age, course load, living distance from campus, computer skills, work status, and first language. Students’ performance, persistence, …

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Map/Ph/1 Queueing Model With Working Vacation And Crowdsourcing, Srinivas R. Chakravarthy, Serife Ozkar Sep 2016

Map/Ph/1 Queueing Model With Working Vacation And Crowdsourcing, Srinivas R. Chakravarthy, Serife Ozkar

Industrial & Manufacturing Engineering Publications

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.

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Preemptive Resume Priority Call Center Model With Two Classes Of Map Arrivals, Srinivas R. Chakravarthy, M. Senthil Kumar, R. Arumuganathan Jan 2013

Preemptive Resume Priority Call Center Model With Two Classes Of Map Arrivals, Srinivas R. Chakravarthy, M. Senthil Kumar, R. Arumuganathan

Industrial & Manufacturing Engineering Publications

Generally in call centers, voice calls (say Type 1 calls) are given higher priority over e-mails (say Type 2 calls). An arriving Type 1 call has a preemptive priority over a Type 2 call in service, if any, and the preempted Type 2 call enters into a retrial buffer (of finite capacity). Any arriving call not able to get into service immediately will enter into the pool of repeated calls provided the buffer is not full; otherwise, the call is considered lost. The calls in the retrial pool are treated alike (like Type 1) and compete for service after a …

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Analysis Of A Multi-Server Queueing Model With Vacations And Optional Secondary Services, Srinivas R. Chakravarthy Jan 2013

Analysis Of A Multi-Server Queueing Model With Vacations And Optional Secondary Services, Srinivas R. Chakravarthy

Industrial & Manufacturing Engineering Publications

In this paper we study a multi-server queueing model in which the customer arrive according to a Markovian arrival process. The customers may require, with a certain probability, an optional secondary service upon completion of a primary service. The secondary services are offered (in batches of varying size) when any of the following conditions holds good: (a) upon completion of a service a free server finds no primary customer waiting in the queue and there is at least one secondary customer (including possibly the primary customer becoming a secondary customer) waiting for service; (b) upon completion of a primary service, …

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Analysis Of A K-Out-Of-N System With Spares, Repairs, And A Probabilistic Rule, Srinivas R. Chakravarthy Sep 2006

Analysis Of A K-Out-Of-N System With Spares, Repairs, And A Probabilistic Rule, Srinivas R. Chakravarthy

Industrial & Manufacturing Engineering Publications

We consider a k-out-of-N reliability system with identical components having exponential lifetimes. There is a single repairman who attends to failed components on a first comefirst-served basis. The repair times are assumed to be of phase type. The system has K spares that can be used according to a probabilistic rule to extend the lifetime of the system. The system is analyzed using Markov chain theory and some interesting results are obtained. A few illustrative numerical examples are discussed.

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Algorithmic Analysis Of The Maximum Level Length In General-Block Two-Dimensional Markov Processes, Jesus R. Artalejo, Srinivas R. Chakravarthy Jun 2005

Algorithmic Analysis Of The Maximum Level Length In General-Block Two-Dimensional Markov Processes, Jesus R. Artalejo, Srinivas R. Chakravarthy

Industrial & Manufacturing Engineering Publications

Two-dimensional continuous-time Markov chains (CTMCs) are useful tools for studying stochastic models such as queueing, inventory, and production systems. Of particular interest in this paper is the distribution of the maximal level visited in a busy period because this descriptor provides an excellent measure of the system congestion. We present an algorithmic analysis for the computation of its distribution which is valid for Markov chains with general-block structure. For a multiserver batch arrival queue with retrials and negative arrivals, we exploit the underlying internal block structure and present numerical examples that reveal some interesting facts of the system.

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Multi-Threshold Control Of The Bmap/Sm/1/K Queue With Group Services, Alexander Dudin N., Srinivas R. Chakravarthy Mar 2003

Multi-Threshold Control Of The Bmap/Sm/1/K Queue With Group Services, Alexander Dudin N., Srinivas R. Chakravarthy

Industrial & Manufacturing Engineering Publications

We consider a finite capacity queue in which arrivals occur according to a batch Markovian arrival process (BMAP). The customers are served in groups of varying sizes. The services are governed by a controlled semi-Markovian process according to a multithreshold strategy. We perform the steady-state analysis of this model by computing (a) the queue length distributions at departure and arbitrary epochs, (b) the Laplace-Stieltjes transform of the sojourn time distribution of an admitted customer, and (c) some selected system performance measures. An optimization problem of interest is presented and some numerical examples are illustrated.

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A K-Out-Of-N Reliability System With An Unreliable Server And Phase Type Repairs And Services: The (N, T) Policy, Srinivas R. Chakravarthy, Achyutha Krishnamoorthy, P. V. Ushakumari Jan 2001

A K-Out-Of-N Reliability System With An Unreliable Server And Phase Type Repairs And Services: The (N, T) Policy, Srinivas R. Chakravarthy, Achyutha Krishnamoorthy, P. V. Ushakumari

Industrial & Manufacturing Engineering Publications

In this paper we study a k-out-of-n reliability system in which a single unreliable server maintains n identical components. The reliability system is studied under the (N,T) policy. An idle server takes a vacation for a random amount of time T and then attends to any failed component waiting in line upon completion of the vacation. The vacationing server is recalled instantaneously upon the failure of the Nth component. The failure times of the components are assumed to follow an exponential distribution. The server is subject to failure with failure times exponentially distributed. Repair times of the component, fixing times …

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Two Parallel Finite Queues With Simultaneous Services And Markovian Arrivals, Srinivas R. Chakravarthy, S. Thiagarajan Jan 1997

Two Parallel Finite Queues With Simultaneous Services And Markovian Arrivals, Srinivas R. Chakravarthy, S. Thiagarajan

Industrial & Manufacturing Engineering Publications

In this paper, we consider a finite capacity single server queueing model with two buffers, A and B, of sizes K and N respectively. Messages arrive one at a time according to a Markovian arrival process. Messages that arrive at buffer A are of a different type from the messages that arrive at buffer B. Messages are processed according to the following rules: 1. When buffer A(B) has a message and buffer B(A) is empty, then one message from A(B) is processed by the server. 2. When both buffers, A and B, have messages, then two messages, one from A …

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A Discrete Single Server Queue With Markovian Arrivals And Phase Type Group Services, Attahiru Sule Alfa, K. Laurie Dolhun, Srinivas R. Chakravarthy Mar 1995

A Discrete Single Server Queue With Markovian Arrivals And Phase Type Group Services, Attahiru Sule Alfa, K. Laurie Dolhun, Srinivas R. Chakravarthy

Industrial & Manufacturing Engineering Publications

We consider a single-server discrete queueing system in which arrivals occur according to a Markovian arrival process. Service is provided in groups of size no more than M customers. The service times are assumed to follow a discrete phase type distribution, whose representation may depend on the group size. Under a probabilistic service rule, which depends on the number of customers waiting in the queue, this system is studied as a Markov process. This type of queueing system is encountered in the operations of an automatic storage retrieval system. The steady-state probability vector is shown to be of (modified) matrix-geometric …

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A Finite Capacity Queue With Markovian Arrivals And Two Servers With Group Services, Srinivas Chakravarthy, Attahiru S. Alfa Feb 1994

A Finite Capacity Queue With Markovian Arrivals And Two Servers With Group Services, Srinivas Chakravarthy, Attahiru S. Alfa

Industrial & Manufacturing Engineering Publications

In this paper we consider a finite capacity queuing system in which arrivals are governed by a Markovian arrival process. The system is attended by two exponential servers, who offer services in groups of varying sizes. The service rates may depend on the number of customers in service. Using Markov theory, we study this finite capacity queuing model in detail by obtaining numerically stable expressions for (a) the steady-state queue length densities at arrivals and at arbitrary time points; (b) the Laplace-Stieltjes transform of the stationary waiting time distribution of an admitted customer at points of arrivals. The stationary waiting …

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