TL;DR: This work provides the first approximate analysis of JSQ in the PS server farm model for general job-size distributions, obtaining the distribution of queue length at each queue by a one-dimensional Markov chain in a novel fashion.
TL;DR: An optimized flooding scheme that minimizes transmission overhead in flooding is introduced and two simple and effective DFT-MSN data delivery schemes are proposed, namely, the replication-based efficient data delivery scheme (RED) and the message fault tolerance-based adaptive data Delivery scheme (FAD).
Abstract: This paper focuses on the delay/fault-tolerant mobile sensor network (DFT-MSN) for pervasive information gathering. We develop simple and efficient data delivery schemes tailored for DFT-MSN, which has several unique characteristics, such as sensor mobility, loose connectivity, fault tolerability, delay tolerability, and buffer limit. We first study two basic approaches, namely, direct transmission and flooding. We analyze their performance by using queuing theory and statistics. Based on the analytic results that show the trade-off between data delivery delay/ratio and transmission overhead, we introduce an optimized flooding scheme that minimizes transmission overhead in flooding. Then, we propose two simple and effective DFT-MSN data delivery schemes, namely, the replication-based efficient data delivery scheme (RED) and the message fault tolerance-based adaptive data delivery scheme (FAD). The RED scheme utilizes the erasure coding technology in order to achieve the desired data delivery ratio with minimum overhead. It consists of two key components for data transmission and message management. The former makes the decision on when and where to transmit data messages according to the delivery probability, which is the likelihood that a sensor can deliver data messages to the sink. The latter decides the optimal erasure coding parameters (including the number of data blocks and the needed redundancy) based on its current delivery probability. The FAD scheme employs the message fault tolerance, which indicates the importance of the messages. The decisions on message transmission and dropping are made based on fault tolerance for minimizing transmission overhead. The system parameters are carefully tuned on the basis of thorough analyses to optimize network performance. Extensive simulations are carried out for performance evaluation. Our results show that both schemes achieve a high message delivery ratio with acceptable delay. The RED scheme results in lower complexity in message and queue management, while the FAD scheme has a lower message transmission overhead.
TL;DR: In this article, the authors describe a queuing system for processing queue data and for providing queue messaging over a network, which includes a first queue configured to hold resource requests from a plurality of users, and program code stored in computer readable memory configured to determine or estimate whether a resource requested by a first resource request submitted by the first requester will be available when the first request will be serviced.
Abstract: Systems and methods are described for processing queue data and for providing queue messaging over a network. An illustrative queuing system includes a first queue configured to hold resource requests from a plurality of users, and program code stored in computer readable memory configured to determine or estimate whether a resource requested by a first resource request submitted by a first requester will be available when the first resource request will be serviced, and to transmit a message over a network to the first requester indicating that the requested resource will not be available when the queued request is serviced if it is estimated or determined that the requested resource will not be available when the first request is serviced.
TL;DR: In this article, the authors present a system and method for processing input/output (I/O) requests in a virtualized computer system, where I/O requests are received from a virtual machine.
Abstract: A system and method for processing input/output (I/O) requests in a virtualized computer system. I/O requests are received from a virtual machine. A set of virtual I/O channels that may be interfaced with a host I/O stack and/or a virtual machine I/O stack adaptively queues requested data using a variety of I/O queue management modules. In one embodiment, the virtual I/O channels include an entropy detection module and a queue storage. The entropy detection module determines an entropy value of specified I/O request data and encodes the specified I/O request data with the entropy value within the queue storage.
TL;DR: In this article, a Simulated Annealing algorithm has been developed to solve the problem of congestion in the M/M/1 queuing system in a hub-and-spoke network.
Abstract: Hub-and-spoke networks are employed in cargo transportation. This paper presents a model for hub location in these kinds of networks. Hubs are considered capacity limited. For that reason, costs due to congestion in hubs are introduced into the model. A Simulated Annealing algorithm has been developed to solve the model. The algorithm includes a balanced module, the purpose of which is to reduce congestion. Each hub is modelled as an M/M/1 queuing system. The algorithm has been tested in randomly created networks. The results show that when a situation of congestion occurs, the proposed algorithm enables better solutions to be found, thereby improving the standard of service.
TL;DR: It is shown that ticket and physical queues have significantly different balking probabilities when customer patience is low and the system traffic is heavy, and an improvement to the ticket queue is proposed that provides each customer with his expected waiting time conditioned on his observed number difference, which is shown to raise the performance of theticket queue to that of the physical queue.
Abstract: Queueing systems managed by ticket technology are widely used in service industries as well as government offices. Upon arriving at a ticket queue, each customer is issued a numbered ticket. The number currently being served is displayed. An arriving customer balks if the difference between his ticket number and the displayed number exceeds his patience level. We propose a Markov chain model of a ticket queue and develop effective evaluation tools. These tools can help management quantify the service level and identify the performance gap between the ticket queue and the conventional physical queue, in which a waiting line is formed. We gain insights about the ways customer service is affected by information loss in the ticket queue. In particular, we show that ticket and physical queues have significantly different balking probabilities when customer patience is low and the system traffic is heavy. We also propose an improvement to the ticket queue that provides each customer with his expected waiting time conditioned on his observed number difference, which is shown to raise the performance of the ticket queue to that of the physical queue.
TL;DR: The Baskets Queue is presented - a new, highly concurrent lock-free linearizable dynamic memory FIFO queue that creates baskets of mixed-order items instead of the standard totally ordered list and outperforms the original MS-queue algorithm in various benchmarks.
Abstract: FIFO Queues have over the years been the subject of significant research. Such queues are used as buffers both in a variety of applications, and in recent years as a key tool in buffering data in high speed communication networks.
Overall, the most popular dynamic-memory lock-free FIFO queue algorithm in the literature remains the MS-queue algorithm of Michael and Scott. Unfortunately, this algorithm, as well as many others, offers no more parallelism than that provided by allowing concurrent accesses to the head and tail. In this paper we present the Baskets Queue - a new, highly concurrent lock-free linearizable dynamic memory FIFO queue. The Baskets Queue introduces a new form of parallelism among enqueue operations that creates baskets of mixed-order items instead of the standard totally ordered list. The operations in different baskets can be executed in parallel. Surprisingly however, the end result is a linearizable FIFO queue, and in fact, we show that a basket queue based on the MS-queue outperforms the original MS-queue algorithm in various benchmarks.
TL;DR: The structure of the profit function and its sensitivity to the variance of the random variable is investigated, and variations of the model are considered according to whether the server can modify the service price after observing the realization of therandom variable.
Abstract: This article deals with the effect of information and uncertainty on profits in an unobservable single-server queuing system. We consider scenarios in which the service rate, the service quality, or the waiting conditions are random variables that are known to the server but not to the customers. We ask whether the server is motivated to reveal these parameters. We investigate the structure of the profit function and its sensitivity to the variance of the random variable. We consider and compare variations of the model according to whether the server can modify the service price after observing the realization of the random variable.
TL;DR: This paper proposes lightweight router mechanisms for identifying and restricting the bandwidth of high-bandwidth best-effort flows that are using a disproportionate share of the bandwidth in times of congestion and describes a sequence of tests capable of suggesting flows for bandwidth regulation.
Abstract: This paper considers the potential negative impacts from an increasing deployment of non-congestion-controlled besteffort traffic on the Internet These negative impacts range from extreme unfairness against competing TCP traffic to the potential for congestion collapse To promote the inclusion of end-to-end congestion control for best-effort traffic, we propose lightweight router mechanisms for identifying and restricting the bandwidth of high-bandwidth best-effort flows that are using a disproportionate share of the bandwidth in times of congestion Our method does not require per-flow state based on packet arrivals, but instead relies on the history of packet drops from a queue with RED (Random Early Detection) queue management Starting with high-bandwidth flows identified from the RED drop history, we describe a sequence of tests capable of suggesting flows for bandwidth regulation These tests additionally identify a high-bandwidth flow in times of congestion as unresponsive, “not TCP-friendly”, or simply veryhigh-bandwidth An unresponsive flow is one failing to reduce its offered load at a router in response to an increased packet drop rate A flow that is not TCP-friendly is one whose long-term arrival rate exceeds that of any conformant TCP in the same circumstances A very-high-bandwidth flow uses a disproportionate share of the bandwidth relative to other flows Simulations show the results of regulating the bandwidth of these unresponsive, TCP-unfriendly, or veryhigh-bandwidth flows in times of congestion We end with a comparison between this approach and others using per-flow scheduling for all best-effort traffic
TL;DR: Extensive ns-2 simulations confirm the effectiveness of the FQA algorithm with respect to the per class QoS enhancement and per-station fair channel sharing in WLAN access networks.
Abstract: As public deployment of wireless local area networks (WLANs) has increased and various applications with different service requirements have emerged, fairness and quality of service (QoS) are two imperative issues in allocating wireless channels. This study proposes a fair QoS agent (FQA) to simultaneously provide per-class QoS enhancement and per-station fair channel sharing in WLAN access networks. FQA implements two additional components above the 802.11 MAC: a dual service differentiator and a service level manager. The former is intended to improve QoS for different service classes by differentiating service with appropriate scheduling and queue management algorithms, while the latter is to assure fair channel sharing by estimating the fair share for each station and dynamically adjusting the service levels of packets. FQA assures (weighted) fairness among stations in terms of channel access time without decreasing channel utilization. Furthermore, it can provide quantitative service assurance in terms of queuing delay and packet loss rate. FQA neither resorts to any complex fair scheduling algorithm nor requires maintaining per-station queues. Since the FQA algorithm is an add-on scheme above the 802.11 MAC, it does not require any modification of the standard MAC protocol. Extensive ns-2 simulations confirm the effectiveness of the FQA algorithm with respect to the per class QoS enhancement and per-station fair channel sharing
TL;DR: In this paper, a device that queues and transmits data packets is described, which includes a queue configured to store data packets awaiting transmission, a controller configured to dynamically determine an order in which the data packets are transmitted from the queue, and a transmission mechanism configured to transmit the data packet from queue in the determined order.
Abstract: A device that queues and transmits data packets is described. This device includes: a queue configured to store data packets awaiting transmission; a controller configured to dynamically determine an order in which the data packets are transmitted from the queue; and a transmission mechanism configured to transmit the data packets from the queue in the determined order. The transmission order is determined using Transmission Control Protocol (TCP) sequence numbers and/or TCP timestamps contained in the data packets in the queue in order to provide increased utility without reducing existing fairness between independent data streams.
TL;DR: In this article, the authors present a system for active queue management of internet-protocol data packets generated in a data packet switched wireless network, which can be effected in a serving base station as well as in an access terminal, and the application that generates the data packets can be executed locally or remotely to either the base station or access terminal.
Abstract: Systems and methods are provided that facilitate active queue management of internet-protocol data packets generated in a data packet switched wireless network. Queue management can be effected in a serving base station as well as in an access terminal, and the application that generates the data packets can be executed locally or remotely to either the base station or access terminal. Management of the generated data packets is effected via a marking/dropping of data packets according to an adaptive response function that can be deterministic or stochastic, and can depend of multiple communication generalized indicators, which include packet queue size, queue delay, channel conditions, frequency reuse, operation bandwidth, and bandwidth-delay product. Historical data related to the communication generalized indicators can be employed to determine response functions via thresholds and rates for marking/dropping data packets.
TL;DR: The queueing scheme that is proposed here forms a natural bridge between the virtual queue size and the physical queue size, and thus extends their result to the stability of the physical queues as well.
Abstract: We propose a new queueing mechanism for coded networks with stochastic arrivals and/or lossy links. In this context, earlier work introduced the notion of "virtual queues" which represent the backlog in degrees of freedom. For instance, the work by Ho and Viswanathan defined the achievable rate region for which the virtual queue size is stabilized, using intra-session coding. The queueing scheme that we propose here forms a natural bridge between the virtual queue size and the physical queue size, and thus extends their result to the stability of the physical queues as well. Specifically, we show that the amount of memory used at the transmit buffer in our scheme is upper bounded by the total backlog in the number of linearly independent degrees of freedom. Moreover, our scheme gives an online algorithm for queue update and coding, in the sense that the coding does not happen block by block, but in a streaming manner. The main idea in our scheme is to ensure that the information stored at the sender excludes any knowledge that is common to all receivers. This requires the transmitting node to track the states of knowledge of its receivers. Therefore, if the links are lossy, some form of feedback may be necessary.
TL;DR: A non-trivial application of the new queue to the performance evaluation of a wireless communication system is presented, along with numerical results, to illustrate the efficacy of the proposed method and the use of negative customers is also demonstrated.
TL;DR: The estimation of arrival and service rates for queues based on queue length data collected at successive, not necessarily equally spaced, time points based on an Ornstein-Uhlenbeck diffusion approximation to the Markov process description of the queue is considered.
Abstract: We consider the estimation of arrival and service rates for queues based on queue length data collected at successive, not necessarily equally spaced, time points. In particular, we consider the M/M/c queue, for c large, but application of the method to the repairman problem is almost identical, and the general approach presented should extend to other queue types. The estimation procedure makes use of an Ornstein-Uhlenbeck diffusion approximation to the Markov process description of the queue. We demonstrate the approach through simulation studies and discuss situations in which the approximation works best.
TL;DR: In this article, the memory controller changes the priority of a request in the first queue in response to a trigger, sends a next scheduled request from the first queuing to the second queue to the memory, and sends requests from the second queuing on the same trigger.
Abstract: A system includes a processor coupled to a memory through a memory controller. The memory controller includes first and second queues. The memory controller receives memory requests from the processor, assigns a priority to each request, stores each request in the first queue, and schedules processing of the requests based on their priorities. The memory controller changes the priority of a request in the first queue in response to a trigger, sends a next scheduled request from the first queue to the second queue in response to detecting the next scheduled request has the highest priority of any request in the first queue, and sends requests from the second queue to the memory. The memory controller changes the priority of different types of requests in response to different types of triggers. The memory controller maintains a copy of each request sent to the second queue in the first queue.
TL;DR: In this article, a buffer allocation algorithm for a plurality of queues of differing priority levels is proposed. But, the algorithm is not suitable for a large number of queues and the buffer allocation is not dynamic.
Abstract: Methods and systems consistent with the present invention provide dynamic buffer allocation to a plurality of queues of differing priority levels. Each queue is allocated fixed minimum number of buffers that will not be de-allocated during buffer reassignment. The rest of the buffers are intelligently and dynamically assigned to each queue depending on their current need. The system then monitors and learns the incoming traffic pattern and resulting drops in each queue due to traffic bursts. Based on this information, the system readjusts allocation of buffers to each traffic class. If a higher priority queue does not need the buffers, it gradually relinquishes them. These buffers are then assigned to other queues based on the input traffic pattern and resultant drops. These buffers are aggressively reclaimed and reassigned to higher priority queues when needed. In this way, methods and systems consistent with the present invention dynamically balance requirements of the higher priority queues versus optimal allocation.
TL;DR: In this paper, an event processor examines the load of each event queue and selects the event queue with the lightest load, such that a user, integration system, or client application does not need to know the identity of the physical queue storing the event, but only needs to refer to the "distributed queue" or alias.
Abstract: High availability event forwarding can be obtained utilizing distributed queues in a server cluster. Each server can receive an event from a data system, such as a database or SAP™ system. Event queues exist on servers in the cluster can store an event until, for example, the event is delivered to a user or retrieved for processing. An event processor examines the load of each event queue and selects the event queue with the lightest load. The event processor generates an alias for the selected queue, such that a user, integration system, or client application does not need to know the identity of the physical queue storing the event, but only needs to refer to the ‘distributed queue’ or alias. After a physical queue is selected and an alias assigned, the event is forwarded to the selected queue.
TL;DR: In this article, the authors describe methods and systems of allowing people to virtually queue in a line via text messaging or mobile phone calls, where the person wishing to get in the line sends a text message or cell phone call to a queuing system or registers via a computer network connection.
Abstract: The disclosure describes methods and systems of allowing people to virtually queue in a line via text messaging or mobile phone calls The person wishing to get in the line sends a text message or cell phone call to a queuing system Alternatively, the person can register via a computer network connection The queuing system then sends a text message back to that person when it is nearly time for them to receive the benefit of being at the front of the line
TL;DR: A queueing model where sometimes the opposite is the case, and it is shown that under Nash equilibrium it is possible (depending on the service distribution) that the joining probability when the queue is empty is smaller than it is when the queues is not empty.
Abstract: The intuition while observing the economy of queueing systems, is that one's motivation to join the system, decreases with its level of congestion. Here we present a queueing model where sometimes the opposite is the case. The point of departure is the standard first-come first-served single server queue with Poisson arrivals. Customers commence service immediately if upon their arrival the server is idle. Otherwise, they are informed if the queue is empty or not. Then, they have to decide whether to join or not. We assume that the customers are homogeneous and when they consider whether to join or not, they assess their queueing costs against their reward due to service completion. As the whereabouts of customers interact, we look for the (possibly mixed) join/do not join Nash equilibrium strategy, a strategy that if adopted by all, then under the resulting steady-state conditions, no one has any incentive not to follow it oneself. We show that when the queue is empty then depending on the service distribution, both `avoid the crowd' (ATC) and `follow the crowd' (FTC) scenarios (as well as none-of-the-above) are possible. When the queue is not empty, the situation is always that of ATC. Also, we show that under Nash equilibrium it is possible (depending on the service distribution) that the joining probability when the queue is empty is smaller than it is when the queue is not empty.
TL;DR: A new AQM algorithm is proposed that considers both the average queue length and the estimated packet arrival rate together in order to detect incipient congestion and has low complexity and easy configuration.
TL;DR: This paper investigates the near-memoryless behavior of the service time for IEEE 802.11 saturated single-hop ad hoc networks and shows that the number of packets successfully transmitted by any node over a time interval follows a general distribution, which is close to a Poisson distribution with an upper bounded distribution distance.
Abstract: This paper investigates the near-memoryless behavior of the service time for IEEE 802.11 saturated single-hop ad hoc networks. We show that the number of packets successfully transmitted by any node over a time interval follows a general distribution, which is close to a Poisson distribution with an upper bounded distribution distance. We also show that the service time distribution can be approximated by a geometric distribution. We illustrate that the usage of discrete-time queuing analysis (M/Geo/1) near network saturation greatly simplifies the queuing analysis and leads to sufficiently accurate results for both the first order statistics and the probability distribution of the number of packets in the queuing system.
TL;DR: In this article, the authors propose an approach for managing bandwidth for a plurality of connections each having a respective connection token, the apparatus having corresponding methods and computer-readable media, comprises a memory to store the connection tokens, the memory comprising a ready connection queue, a pending increase connection queuing, and an increase connection queue; and a controller to move connection tokens in the ready connection queue to the pending increase connect queue when bandwidth for the respective connections should be increased.
Abstract: Apparatus for managing bandwidth for a plurality of connections each having a respective connection token, the apparatus having corresponding methods and computer-readable media, comprises a memory to store the connection tokens, the memory comprising a ready connection queue, a pending increase connection queue, and an increase connection queue; and a controller to move connection tokens in the ready connection queue to the pending increase connection queue when bandwidth for the respective connections should be increased; wherein the controller moves connection tokens in the pending increase connection queue to the increase connection queue, and increases bandwidth for the respective connections, when a number of the connection tokens in the increase connection queue is less than a predetermined maximum number; and wherein the controller moves connection tokens in the increase connection queue to the ready connection queue when bandwidth for the respective connections should be decreased.
TL;DR: In this paper, a plurality of queues through the transport system is defined, and each vehicle is assigned to one of the plurality and a period of time each vehicle remains in the queue.
Abstract: Methods and systems for controlling vehicular traffic flow in a transport system are provided. The method includes defining a plurality of queues through the transport system, assigning each of a plurality of vehicles into one of the plurality of queues, determining a number of vehicles in each queue and a period of time each vehicle remains in the queue, and permitting traffic flow in at least one queue that facilitates reducing the congestion of the plurality of queues.
TL;DR: In this article, a virtual queuing system and a method for dynamic control of queue data in accordance with queue control instructions provided by a separate queue control source is presented, where the queue data is provided to the control source by an interface to the queue system.
Abstract: A virtual queuing system and method provides for dynamic control of queue data in accordance with queue control instructions provided by a separate queue control source. The virtual queuing system comprises an interface to a queuing system and an interface to the separate queue control source. The interface to the queuing system provides for obtaining queue data and controlling the queue data in accordance with the queue control instructions provided by a separate queue control source. The interface to the separate queue control source for: i) providing the queue data to the separate queue control source; and ii) obtaining the queue control instructions there from.
TL;DR: The Access Point Queue (APQ) methodology for externally estimating the queue capacity for a wireless AP is presented and deployed and the wireless AP queue capacities are shown to be packet-based and to range from 50 packets to over 350 packets.
Abstract: While queue capacities have a direct impact on loss and latency during congestion, and wireless networks continue to spread in university, corporate and home networks, little is publicly known about the queue capacities of wireless access points (APs). This paper presents and deploys the Access Point Queue (APQ) methodology for externally estimating the queue capacity for a wireless AP. APQ determines the AP saturation point, measures the baseline delay, induces the saturation rate to measure the delay with a full AP queue and computes the queue capacity. APQ is deployed to determine the queue capacities of three commercial class and four residential class APs. The wireless AP queue capacities are shown to be packet-based and to range from 50 packets to over 350 packets. The fact that queue capacities vary so much among devices targeted for the same network configuration suggests future work to determine the most appropriate queue capacity.
TL;DR: In this paper, a method and system for scheduling tasks in a processing system is presented, which comprises processing tasks from a primary work queue, wherein the tasks consume resources that are operable to be released.
Abstract: A method and system for scheduling tasks in a processing system. In one embodiment, the method comprises processing tasks from a primary work queue, wherein the tasks consume resources that are operable to be released. Whenever the volume of resources that have been consumed exceeds a threshold, the processor executes tasks from a secondary work queue for a period of time. The secondary work queue is comprised of tasks from the primary work queue that can release the resources; the secondary work queue can be sorted according to the volume of resources that can be released.
TL;DR: The proposed PQ-MAC protocol is an energy-efficient, priority-based, and QoS compatible MAC protocol which consists of multi-level queue management, sleep-wakeup scheduling, and an ordered contention period (CP) scheme that guarantees time-bounded delivery of QoS packets.
Abstract: In this letter, we propose PQ-MAC: a priority-based medium access control (MAC) protocol for providing quality of service (QoS) in wireless sensor networks (WSNs) which minimizes the energy consumption with traffic-based sleep-wakeup scheduling and supports QoS using differentiating channel access policy, packet scheduling, and queue management. The PQ-MAC utilizes the advantages of time division multiple access (TDMA) and slotted carrier-sense multiple access (CSMA). The proposed protocol is an energy-efficient, priority-based, and QoS compatible MAC protocol. It consists of multi-level queue management, sleep-wakeup scheduling, and an ordered contention period (CP) scheme. It also guarantees time-bounded delivery of QoS packets. Performance evaluation is conducted between PQ-MAC and S-MAC with respect to three performance metrics: energy consumption, throughput, and average latency. The simulation results show that the performance of PQ-MAC is better than that of S-MAC.
TL;DR: A priority-based queuing model is examined and the mathematical analysis of different media calls processing in converged network environment is performed and results of the expected response and waiting time are presented.
Abstract: Converged network seamlessly integrates different communications media such as data, voice and multimedia on a single platform It refers to convergence both types of network and technologies as well as convergence between the different layers of network architecture In this paper, we examine a priority-based queuing model and perform the mathematical analysis of different media calls processing in converged network environment We use for this purpose a queuing system model M3/G3/1/NPRP in order to process effectively input jobs/requests (or packets) Tasks within this queuing system get a higher priority if they are handling a real-time event We present in our paper mathematical results of the expected response and waiting time, and build hypothetical diagrams for the further practical usage in real-time system A modeling method developed in this paper will be used for the fast configuration and testing of new converged network applications and services
TL;DR: A novel integrated analytical framework for analyzing the quality-of-service (QoS) performance measures in a wireless mobile multimedia network that integrates physical, radio link, and network layer parameters and protocols to analyze the call-level and packet-level performances.
Abstract: We present a novel integrated analytical framework for analyzing the quality-of-service (QoS) performance measures in a wireless mobile multimedia network. The framework integrates physical, radio link, and network layer parameters and protocols to analyze the call-level and packet-level performances. In the network layer, call admission control (CAC) is responsible for deciding whether an incoming call can be accepted or not so that the performances of the ongoing calls do not deteriorate below the acceptable level. Also, an adaptive channel allocation (ACA) scheme is used to maximize the utilization of the radio resources. In the data link layer, queue management and error control are used for non-real-time loss-sensitive traffic. In the physical layer, a finite state Markov channel (FSMC) is used to model channel fading, and adaptive modulation is used for rate adaptation according to channel quality. Various call-level and packet-level QoS measures for real-time, non-real-time, and best-effort traffic are obtained. The analytical results are validated by extensive simulations. Examples of the applications of the presented analytical framework are also provided