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This article explores the performance of interconnected queueing systems and queueing-inventory systems (IQSQIS) in stochastic modeling. IQSQIS features two types of service facilities with dual service stations: one providing non-commodity service with a multi-server, and another handling commodity sales with a single server. As directed, a customer type i,i=1,2 can approach the station i,i=1,2 whose arrival pattern follows the marked Markovian arrival process (MMAP) since we assume that both service stations have an equal arrival phase. The IQSQIS gives an offer to the type-2 customer to choose type-1 service at the end of their service completion. Numerical results suggest that this option reduces customer wait times, orbit size, and overall system costs. The comparative analysis of heterogeneous and homogeneous servers in station-1 and queue-dependent and non-queue-dependent service facilities in station-2 is presented and investigated using the numerical outputs.

This study aims to derive analytical expressions for temperature, concentration, and velocity in an unsteady MHD convective nanofluid flow past a moving vertical plate. The governing nonlinear differential equations are solved analytically using the Homotopy Analysis Method (HAM). The resulting solutions are presented as concentration, temperature, and velocity profiles, allowing for the analysis of various physical parameters' influence on the flow behavior. Furthermore, our analytical results are validated by comparing them with existing numerical solutions using MATLAB. The impact of these parameters on skin friction, the Nusselt number, and the Sherwood number is presented, demonstrating good agreement with previously reported data. The findings of this research hold significance for industries involving heat transfer processes, such as thermal management systems, electronic cooling, and energy generation applications.

The two service stations have been connected in series in our tandem queueing inventory model, replicating the real-life environment that provides customer service by providing seperated service without congestion. Customers arrive at Station 1, which has infinite servers (self-service), according to the Markovian arrival process, where they get an information about the inventory. After completion of service in Station 1, the customers can choose whether to move to the buffer in front of Station 2, where a single server gives service for buying inventory, or can exit the system with the predetermined probability. Once the customer who demands an inventory enters the buffer, they are instantly attached to an inventory from the unattached inventory of maximum capacity S, and the inventory replenishment follows $ (s, Q) $ ordering policy. In Station 2, the server provides two services that the customers can choose with a predefined probability. The server in Station 2 may break down at any time during service. When the server experiences the empty buffer, the server automatically moves to vacation until it finds the customer in the system. Exponentially distributed service, lead, breakdown, and repair times have been considered. The joint probability distribution of the number of customers in Station 1, the available inventory level, and the number of customers in the Station 2 buffer has been found. Numerical calculations have been done to show the sensitive analysis of all parameters.

This paper considers a stochastic queueing-inventory system with dual service stations, two groups of heterogeneous multi-servers, two finite waiting halls, and two classes of customers. Station-1 and station-2 provide an inventory sales service and feedback service, respectively. The feedback service option can be given to customers at the service completion epoch. If a customer requires feedback service, moves to an orbit; otherwise, leaves the system permanently. The classical retrial policy is applied to get feedback service. For the replenishment process, the system follows an (S−1,S) base stock ordering policy. This study analyzes the model under four classifications: 1) orbit size is finite and servers have homogeneous service rate; 2) orbit size is finite and servers have heterogeneous service rate; 3) orbit size is infinite and servers have homogeneous service rate; and 4) orbit size is infinite and servers have heterogeneous service rate. The steady-state probability vector for an infinite-size orbit case is computed using the Neuts and Rao truncation method. An expected total cost function is derived with sufficient system indicators for the four classifications. An optimized expected total cost is gained for classifications 2 and 4. The probability that a server is busy, the customer's waiting time, and the customer's loss rate are minimized for classifications 2 and 4.

Let G′ be a simple, connected, and undirected (UD) graph with the vertex set M(G′) and an edge set N(G′). In this article, we define a function f:M∪N⟶0,1 as a fractional mixed dominating function (FMXDF) if it satisfies fRmx=∑yϵRmxfy≥1 for all x∈MG′∪NG′, where Rmx indicates the closed mixed neighbourhood of x, that is the set of all y∈MG′∪NG′ such that y is adjacent to x and y is incident with x and also x itself. Here, pf=∑x∈M∪Nfx is the poundage (or weight) of f. The fractional mixed domination number (FMXDN) is denoted by γfm∗G′ and is designated as the lowest poundage among all FMXDFs of G′. We compute the FMXDN of some common graphs such as paths, cycles, and star graphs, the middle graph of paths and cycles, and shadow graphs. Furthermore, we compute upper bounds for the sum of the two fractional dominating parameters, resulting in the inequality γf1′Τ+γfm∗Τ≤r+p−radΤ−α, where γf1′ and γfm∗ are the fractional edge domination number and FMXDN, respectively. Finally, we compare γfm∗ to other resolvability-related parameters such as metric and fault-tolerant metric dimensions on some families of graphs.

In order to ensure that only the designated person can verify the signer's signature on the message, Steinfeld et al. introduced the concept of Universal Designated Verifier Signature (UDVS), which enables a designator who has obtained a signature on a message from the signer to designate the signature to any desired designated verifier. This idea was developed to address the privacy concerns of the signature holder at the time of certificate distribution. They are appropriate for applications that demand the designer's secrecy. The fact that the designated verifier must generate a public key with regard to the signer's public parameter for signature verification is a significant drawback of UDVS methods. In cases where the verifier is unable to begin the key generation procedure, this constraint is inapplicable. Baek et al. developed the idea of "Universal Designated Verifier Signature Proof (UDVSP)", which does not require the verifier's public key for verification, to get around this restriction. All existing UDVSP constructions are based on a discrete logarithm problem, which is vulnerable to quantum computer attacks. As a result, an efficient quantum resistant UDVSP is built on a hard problem in coding theory, as suggested by NIST reports. The scheme's security against forgeability and impersonation attacks is examined using the random oracle model.

The vast majority of engineering issues, particularly heat transport equations, have a non-linear form. The analytical solution of temperature distribution, fin effectiveness, and fin efficiency of straight convective fins that transport heat with temperature-dependent thermal conductivity convection is derived in this work using the Direct Akbari-Ganji method (DAGM). DAGM is an effective methodology that is very simple and takes less time to solve non-linear temperature distribution fin problems. In the present investigation, Direct Akbari-Ganji technique offers desirable solutions to heat transfer problems. The round-off error is smaller compared to other methods. For the purpose of calibrating the error accuracy of the suggested direct technique, this result is compared with the numerical and earlier solution. The outcomes show that the DAGM for heat transfer equations in engineering situations has excellent validity and considerable promise. Finally, it is clear that when the thermo-geometric fin parameter increases, so does the fin efficiency. The homogeneity of the fin is due to the variable thermal conductivity. Four convection conditions with constant coefficients, growing and decaying convection coefficient with fin temperature are discussed.

This study investigates a multi-server queueing-inventory system in a random environment. The system has an unlimited waiting space and an inventory capacity of $S$ units. The customer arrives at the system according to the Markovian arrival process. Whenever all the servers are busy, an arriving customer either goes to an unlimited waiting space or leaves the system. And if there is a free server with positive inventory, then the arriving customer gets service immediately. Inventories are filled under the instantaneous replenishment policy. We consider that the service time follows a phase-type distribution, and we assess the joint probability distribution of the inventory level and the number of customers in the steady-state case. On top of that, we extract the sojourn time distributions of arbitrary customers using the Laplace-Stieltjes transform. Finally, a few numerical examples are provided to illustrate our mathematical model.

In recent times, we have encountered new situations that have imposed restrictions on our ability to visit public places. These changes have affected various aspects of our lives, including limited access to supermarkets, vegetable shops, and other essential establishments. As a response to these circumstances, we have developed a continuous review retrial queueing–inventory system featuring a single server and controlled customer arrivals. In our system, customers arriving to procure a single item follow a Markovian Arrival Process, while the service time for each customer is modeled by an exponential distribution. Inventories are replenished according to the (s,Q) reordering policy with exponentially distributed lead times. The system controls arrival in the waiting space with setup time. The customers who arrive at a not allowed situation decide to enter an orbit of infinite size with predefined probability. Orbiting customers make retrials to claim a place in the waiting space, and their inter-retrial times are exponentially distributed. The server may experience essential interruption (emergency situation) which arrives according to Poisson process. Then, the server goes for an emergency vacation of a random time which is exponentially distributed. In the steady-state case, the joint probability of the number of customers in orbit and the inventory level has been found, and the Matrix Geometric Method has been used to find the steady-state probability vector. In numerical calculations, the convexity of the system and the impact of F-policy and emergency vacation in the system are discussed.

The real-time vehicular traffic system is an integral part of the urban vehicular traffic system, which provides effective traffic signal control for a large multifaceted traffic network and is a highly challenging distributed control problem. Coordinating vehicular traffic enables the network model to deliver an efficient service flow. Consider that there are four lanes of vehicular traffic in this situation, allowing parallel vehicle movements to occur without causing an accident. In this instance, the vehicular system’s control parameters are time and vehicle volume. In this work, vehicular traffic flow is examined, and an algorithm to estimate vehicle waiting time in each direction is estimated. The effectiveness of the proposed vehicle traffic signal distribution control system by comparing the experimental results with a real-time vehicular traffic system is verified. This is also illustrated numerically.

This paper investigates the queue-dependent service rates(QDSR) in the stochastic queueing-inventory system(SQIS). This SQIS consists a single server service channel, S number of inventories, and a finite queue. An arriving customer gets the service immediately if the server is free and there exists a positive stock in the SQIS. When the server is busy, they have to wait in the finite queue. Suppose they find that the waiting hall is full, either they leave the system or enter into an infinite orbit under the Bernoulli trial. The service rate of any arrival is dependent on the number of customers in the queue at present. The orbital customer can compete for the service only through joining into the waiting hall based on the classical retrial policy. Whenever the number of inventories in SQIS is reached a certain limit s, the replenishment of Q(=S−s) items is placed. Due to the structure of rate matrix, the stability analysis, minimal non-negative solutions of the quadratic systems are derived through the Neuts matrix-geometric approximation(MGA). Further, the waiting time distribution(WTD) of arrival and necessary system characteristics are derived. Finally, adequate numerical examples are presented to highlight the proposed SQIS.

Graph theory is a useful mathematical structure used to model pairwise relations between sensor nodes in wireless sensor networks. Graph equations are nothing but equations in which the unknown factors are graphs. Many problems and results in graph theory can be formulated in terms of graph equations. In this paper, we solved some graph equations of detour two-distance graphs, detour three-distance graphs, detour antipodal graphs involving with the line graphs.

This article analyses a four-dimensional stochastic queueing-inventory system with multiple server vacations and a state-dependent arrival process. The server can start multiple vacations at a random time only when there is no customer in the waiting hall and the inventory level is zero. The arrival flow of customers in the system is state-dependent. Whenever the arriving customer finds that the waiting hall is full, they enter into the infinite orbit and they retry to enter the waiting hall. If there is at least one space in the waiting hall, the orbital customer enters the waiting hall. When the server is on vacation, the primary (retrial) customer enters the system with a rate of λ1(θ1). If the server is not on vacation, the primary (retrial) arrival occurs with a rate of λ2(θ2). Each arrival rate follows an independent Poisson distribution. The service is provided to customers one by one in a positive time with the rate of μ, which follows exponential distribution. When the inventory level drops to a fixed s, reorder of Q items is triggered immediately under (s,Q) ordering policy. The stability of the system has been analysed, and using the Neuts matrix geometric approach, the stationary probability vectors have been obtained. Moreover, various system performance measures are derived. The expected total cost analysis explores and verifies the characteristics of the assumed parameters of this model. The average waiting time of a customer in the waiting hall and orbit are investigated using all the parameters. The monotonicity of the parameters is verified with its characteristics by the numerical simulation. The discussion about the fraction time server being on vacation suggests that as the server’s vacation duration reduces, its fraction time also reduces. The mean number of customers in the waiting hall and orbit is reduced whenever the average service time per customer and average replenishment time are reduced.

The purpose of this article is to examine the server activation policy (SAP) in a multi-server queuing-inventory system (MQIS). The queue has a total of c number of multi-threshold stages as well as c-homogeneous servers. The activation of each server begins one by one if there is an adequate queue length and inventory in the system; otherwise, they remain idle. The server deactivation process continues until the queue length exceeds the manageable level (predetermined stages) or there is insufficient stock. In addition, when we assume the length of the two successive threshold levels is one, the server activation policy model becomes a regular multi-server model. The Neuts matrix geometric approach is used to discuss the stability condition, stationary probability vector. The Laplace–Stieltjes transform (LST) is used to analyse the waiting time distributions of the queue and orbital customers. Additionally, significant system performance metrics and sensitivity analysis are used to investigate the effects of various parameters and cost values. In the comparative result between the server activation model (SAM) and without the server activation model (WSAM) on the expected total cost, we obtain the minimised cost in the SAM. Moreover, the results are obtained by assuming that the length of the intervals between the two successive threshold levels is to be taken into account as the non-uniform length. The expected inventory level, reorder rate, and waiting time of a customer in the waiting hall and orbit were explored numerically by the parameter analysis.

The use of a Markovian inventory system is a critical part of inventory management. The purpose of this study is to examine the demand for two commodities in a Markovian inventory system, one of which is designated as a major item (Commodity-I) and the other as a complimentary item (Commodity-II). Demand arrives according to a Poisson process, and service time is exponential at a queue-dependent rate. We investigate a strategy of (s,Q) type control for commodity-I with a random lead time but instantaneous replenishment for commodity-II. If the waiting hall reaches its maximum capacity of N, any arriving primary client may enter an infinite capacity orbit with a specified ratio. For orbiting consumers, the classical retrial policy is used. In a steady-state setting, the joint probability distributions for commodities and the number of demands in the queue and the orbit, are derived. From this, we derive a waiting time analysis and a variety of system performance metrics in the steady-state. Additionally, the physical properties of various performance measures are evaluated using various numerical assumptions associated with diverse stochastic behaviours.

This paper explores the random environment with two classes of suppliers and impulse customers. The system’s greatest inventory size is S, and it has an infinitely large orbit. In this case, there are two categories of suppliers: temporary suppliers and regular suppliers. Whenever the inventory approaches r, we place on order Q1 (=S−r) unit items to a temporary supplier. Similarly, when the inventory level drops to s (s+1) units of items to our regular supplier. Two types of suppliers’ lead times are considered to be exponentially distributed. Here, the customers who arrive from different states of the random environment (RE) are followed by the Markovian arrival process. If there is no inventory in the system when the customer arrives, they are automatically assigned to an orbit. The model was examined in steady state by using the matrix-analytic approach. Finally, the numerical examples for our structural model are discussed.

A set S⊆V of a graph G=V,E is called a co-independent liar’s dominating set of G if (i) for all v∈V, NGv∩S≥2, (ii) for every pair u,v∈V of distinct vertices, NGu∪NGv∩S≥3, and (iii) the induced subgraph of G on V−S has no edge. The minimum cardinality of vertices in such a set is called the co-independent liar’s domination number of G, and it is denoted by γcoiLRG. In this paper, we introduce the concept of co-independent liar’s domination number of the middle graph of some standard graphs such as path and cycle graphs, and we propose some bounds on this new parameter.

Digital signatures are unsuitable for specific applications that are sensitive on a personal or commercial level because they are universally verifiable. Jakobsson et al. proposed the Designated Verifier Signature (DVS) system, which only allows the intended verifier to validate a message’s signature. It prohibits the disclosure of a conviction to a third party. This functionality is useful in applications that require both authenticity and signer privacy, such as electronic voting and tender calls. The vast majority of current DVS schemes are based on difficult number theory problems such as integer factorization or discrete log problems over various groups. The development of a large-scale quantum computer would render these schemes unsafe. As a result, it is critical to develop quantum-resistant DVS methods. In both quantum and classical computers, signatures based on one-way functions are more efficient and secure. They have several advantages over digital signatures based on trapdoor functions. As a result, hash-based signatures are now considered viable alternatives to number-theoretic signatures. Existing hash-based signatures, on the other hand, are easily verifiable by anyone. As a result, they do not protect the signer’s identity. In addition, they are one-time signatures. This paper presents a hash-based multi-time designated verifier signature scheme that ensures signer anonymity. The unforgeability of the signature scheme is also tested in the random oracle model under chosen message attack. The properties such as non-transferability and non-delegatability are investigated.

This research analyses the performance of a perishable queueing-inventory system for two commodities with optional customers demands. We assume in the article that all customers who come to the system can only purchase the first item or the second item or service (they do not purchase both items). This is the original aspect of the paper. We show the significance of the impact of optional demands on the system’s performance, which is the purpose of the paper. In this system, customers arrive, using the Markovian arrival process (MAP), to a demand for a single unit. The system is composed of a waiting hall with a limited capacity of F. The arriving customer observes the waiting hall is filled to capacity or the stock stage is zero, and they decide to leave the system. In the steady-state case, the joint probability distribution for the first commodity, the second commodity, and the number of customers in the system are computed using matrix geometric methods. We evaluate diverse system performance measures. Finally, we provide a numerical illustration of the optimal value for diverse parameters of the system, which highlights the results and implications of the article.

This paper deals with an integrated and interconnected stochastic queuing-inventory system with a fresh item, a returned item, and a refurbished item. This system provides a multi-type service facility to an arriving multi-class customer through a dedicated channel. It sells fresh and refurbished items, buys used items from customers, refurbishes the used items for resale, and provides a repair service for defective items. The assumption of purchasing a used item from the customer and allowing them to buy a fresh item is a new idea in stochastic queuing-inventory modeling. To do so, this system has four parallel queues to receive four classes of customers and five dedicated servers to provide a multi-type service facility. Customers are classified according to the type of service they require. Each class of arrival follows an independent Poisson process. The service time of each dedicated server is assumed to be exponentially distributed and independent. This system assumes an instantaneous ordering policy for the replenishment of a fresh item. In the long run of this considered system, the joint probability distribution of the seven-dimensional stochastic process, significant system performance measures, and the optimum total cost are to be derived using the Neuts matrix geometric technique. The main objective of the system was to increase the occurrence of all kinds of customers by providing a multi-type service facility in one place. Buying a used item is unavoidable in an emerging society because it helps form a green society. Furthermore, the numerical result shows that the assumption of a system that allows a customer to sell their used item and purchase a new item will increase the number of customers approaching the system.

As a standard digital signature may be verified by anybody, it is unsuitable for personal or economically sensitive applications. The chameleon signature system was presented by Krawczyk and Rabin as a solution to this problem. It is based on a hash then sign model. The chameleon hash function enables the trapdoor information holder to compute a message digest collision. The holder of a chameleon signature is the recipient of a chameleon signature. He could compute collision on the hash value using the trapdoor information. This keeps the recipient from disclosing his conviction to a third party and ensures the privacy of the signature. The majority of the extant chameleon signature methods are built on the computationally infeasible number theory problems, like integer factorization and discrete log. Unfortunately, the construction of quantum computers would be rendered insecure to those schemes. This creates a solid requirement for construct chameleon signatures for the quantum world. Hence, this paper proposes a novel quantum secure chameleon signature scheme based on hash functions. As a hash-based cryptosystem is an essential candidate of a post-quantum cryptosystem, the proposed hash-based chameleon signature scheme would be a promising alternative to the number of theoretic-based methods. Furthermore, the proposed method is key exposure-free and satisfies the security requirements such as semantic security, non-transferability, and unforgeability.

The COVID-19 pandemic has spread to almost all countries of the World and affected people both mentally and economically. The primary motivation of this research is to construct a model that takes reviews or evaluations from several people who are affected with COVID-19. As the number of cases has accelerated day by day, people are becoming panicked and concerned about their health. A good model may be helpful to provide accurate statistics in interpreting the actual records about the pandemic. In the proposed work, for sentimental analysis, a unique classifier named the Sentimental DataBase Miner algorithm (SADBM) is used to categorize the opinions and parallel processing, and is applied on the data collected from various online social media websites like Twitter, Facebook, and Linkedin. The accuracy of the proposed model is validated with trained data and compared with basic classifiers, such as logistic regression and decision tree. The proposed algorithm is executed on CPU as well as GPU and calculated the acceleration ratio of the model. The results show that the proposed model provides the best accuracy compared with the other two models, i.e., 96% (GPU).

Consider the Diophantine equation yn=x+x(x+1)+⋯+x(x+1)⋯(x+k), where x, y, n, and k are integers. In 2016, a research article, entitled – ’power values of sums of products of consecutive integers’, primarily proved the inequality n= 19,736 to obtain all solutions (x,y,n) of the equation for the fixed positive integers k≤10. In this paper, we improve the bound as n≤ 10,000 for the same case k≤10, and for any fixed general positive integer k, we give an upper bound depending only on k for n.

In this study, we consider a perishable inventory system that has an (s, Q) ordering policy, along with a finite waiting hall. The single server, which provides an item to the customer after completing the required service performance for that item, only begins serving after N customers have arrived. Impatient demand is assumed in that the customers waiting to be served lose patience and leave the system if the server’s idle time overextends or if the arriving customers find the system to be full and will not enter the system. This article analyzes the impatient demands caused by the N-policy server to an inventory system. In the steadystate, we obtain the joint probability distribution of the level of inventory and the number of customers in the system. We analyze some measures of system performance and get the total expected cost rate in the steadystate. We present a beneficial cost function and confer the numerical illustration that describes the impact of impatient customers caused by N-policy on the inventory system’s total expected cost rate.

Aim: To evaluate the efficacy of locally delivered nanomedicine, vasoactive intestinal peptide in sterically stabilized micelles (VIP-SSM) to the colon and conduct in vitro release studies of a potential oral formulation. Materials & methods: Intracolonic instillation of VIP-SSM was tested in a mouse model of dextran sulfate sodium-induced colitis. Based on the effective mouse dose, human equivalent dose containing nanomedicine powder was filled into enteric coated capsules for in vitro release testing. Results: Colonic delivery of VIP-SSM significantly alleviated colitis. VIP-SSM containing capsules completely dissolved at colonic pH allowing micelles to reform with active VIP. Capsule formulations exhibited reproducible release profiles when stored up to 6 weeks demonstrating stability. Conclusion: VIP-SSM is an effective nanomedicine formulation which appears to have potential for oral treatment of colitis in humans. [ABSTRACT FROM AUTHOR]