G-Networks: Development of the Theory of Multiplicative Networks

This is a review on G-networks, which are the generalization of the Jackson and BCMP networks, for which the multi-dimensional stationary distribution of the network state probabilities is also represented in product form. The G-networks primarily differ from the Jackson and BCMP networks in that they additionally contain a flow of the so-called negative customers and/or triggers. Negative customers and triggers are not served. When a negative customer arrives at a network node, one or a batch of positive (ordinary) customers is killed (annihilated, displaced), whereas a trigger displaces a positive customer from the node to some other node. For applied mathematicians, G-networks are of great interest for extending the multiplicative theory of queueing networks and for practical specialists in modeling computing systems and networks and biophysical neural networks for solving pattern recognition and other problems.     

The stationary distribution invariance of states in a closed queueing network with temporarily non-active customers

A stationary functioning of a closed queueing network with temporarily non-active customers is analyzed. Non-active customers are located at network nodes in queues, being not serviced. For a customer, the feasibility of passing from its ordinary state to the temporarily non-active state (and backwards) is provided. Service times of customers at different nodes possess arbitrary distributions. Finally, the stationary distribution invariance of network states is established with respect to the functional form of customer service time distributions under fixed first-order moments.     

Delays in a series of queues with correlated service times

In almost all applications of queueing network models it is assumed that for each customer the service times at different network nodes are independent. But service times in, for instance, computer and communication networks are typically essentially determined by properties like message or packet lengths that do not change substantially on the route through the network. Therefore, the service times of any customer in a queueing network are likely to be correlated, which can significantly influence quality of service (QoS) properties and performance measures such that results obtained with the independence assumption may be misleading. We consider delays in a series of queues with correlated service times at each network node where for each customer the service time at the first node is a random variable and the successive service times are correlated with the one at the first node. A recursive scheme for delays is provided. This scheme is used in order to efficiently conduct a simulation study where two types of correlation are studied, namely identical service times, and service times with an additional Gaussian noise. The simulation study focuses on comparisons of end-to-end delays for independent service times at different nodes and correlated service times, respectively. It turns out that for both correlation types, in light traffic the delays in case of correlated service times are larger than for independent service times by a factor that first increases with increasing traffic intensity up to a maximum value approached in medium traffic after which it decreases quickly and drops down to become significantly smaller than one in heavy traffic. This effect intensifies with increasing number of network nodes and depends, as well as the crossover point from which on correlated service times yield smaller delays, on the distribution of the service times at the first node.     

Response times in a two-node queueing network with feedback

The study presented in this paper is motivated by the performance analysis of response times in distributed information systems, where transactions are handled by iterative server and database actions. We model system response times as sojourn times in a two-node open queueing network with a processor sharing (PS) node and a first-come-first-served (FCFS) node. External customers arrive at the PS node according to a Poisson process. After departing from the PS node a customer proceeds to the FCFS node with probability p, and with probability 1−p the customer departs from the system. After a visit to the FCFS node, customers are fed back to the PS node. The service requirements at both nodes are exponentially distributed. The model is a Jackson network, admitting a product-from solution for the joint number of customers at the nodes, immediately leading to a closed-form expression for the mean sojourn times in steady-state. The variance of the sojourn times, however, does not admit an exact expression—the complexity is caused by the possibility of overtaking. In this paper we propose a methodology for deriving simple, explicit and fast-to-evaluate approximations for the variance of the sojourn times. Numerical results demonstrate that the approximations are very accurate in most model instances.     

Insensitivity in processor-sharing networks

We consider an open network of processor-sharing nodes with state-dependent service capacities, i.e., the speed of each node may depend on the number of customers at any node. We demonstrate that the stationary distribution of the network state is insensitive to the distribution of service times if and only if the service capacities are balanced, i.e., the considered network is a Whittle network. The stationary distribution then has a closed-form expression and the expected sojourn time of a customer at any node is proportional to its required quantity of service. These results are extended to the cases of closed networks and state-dependent arrival rates and routing. Two simple examples illustrate the practical interest of these results in the context of communication networks.     

A Two-Queue Polling Model with Two Priority Levels in the First Queue

In this paper we consider a single-server cyclic polling system consisting of two queues. Between visits to successive queues, the server is delayed by a random switch-over time. Two types of customers arrive at the first queue: high and low priority customers. For this situation the following service disciplines are considered: gated, globally gated, and exhaustive. We study the cycle time distribution, the waiting times for each customer type, the joint queue length distribution at polling epochs, and the steady-state marginal queue length distributions for each customer type.     

Assessment of system reliability for a stochastic-flow distribution network with the spoilage property

In supply chain management, satisfying customer demand is the most concerned for the manager. However, the goods may rot or be spoilt during delivery owing to natural disasters, inclement weather, traffic accidents, collisions, and so on, such that the intact goods may not meet market demand. This paper concentrates on a stochastic-flow distribution network (SFDN), in which a node denotes a supplier, a transfer station, or a market, while a route denotes a carrier providing the delivery service for a pair of nodes. The available capacity of the carrier is stochastic because the capacity may be partially reserved by other customers. The addressed problem is to evaluate the system reliability, the probability that the SFDN can satisfy the market demand with the spoilage rate under the budget constraint from multiple suppliers to the customer. An algorithm is developed in terms of minimal paths to evaluate the system reliability along with a numerical example to illustrate the solution procedure. A practical case of fruit distribution is presented accordingly to emphasise the management implication of the system reliability.     

The Effects of the Service Environment on Perceived Waiting Time and Emotions

Because customers’ experience of waiting for service may negatively affect their behavioral approach toward the service organization, improving the service environment may also improve their waiting experience. This study examined the different effects of environmental elements on the perceived waiting time route and the emotional route. We surveyed 326 customers of a leading fast‐food chain restaurant in Taiwan during rush hour. We found that the emotional route is a stronger predictor of customer approach behavior than the perceived waiting time route. Moreover, the explained wait and perceived crowding directly affect both the perceived waiting time route and the emotional route. The effect of the design factor on the customer behavior approach is significant in the emotional route, but it is not significant in the perceived waiting route. In addition, perceived crowding has the strongest effect on the perceived waiting time route, and the explained wait has the strongest effect on the emotional route.     

An open exponential queuing network with limited waiting spaces and losses: A method of approximate analysis

Open exponential queuing networks are considered where each node in a network represents several exponential servers with a joint waiting space (a buffer) of limited capacity. A customer arriving to a node with fully occupied buffer is lost. An assumption is made that the input flow to each node formed as a mixture of the external Poisson flow and the flows coming from other nodes is a Poisson flow. Under this assumption, a method of computing network parameters is presented which is based on solving iteratively a system of nonlinear equations for the unknown nodal flow rates. A method based on Markov chain techniques is presented to find the approximate value of the average conditional sojourn time in the network for customers which completed their service process in the network and for customers which were lost eventually. It is demonstrated for two types of a network (a complete 5-node graph and a 5-node tandem-type system) that the network parameters obtained by the derived analytic method are close to those obtained by the Monte Carlo simulation method.     

Invariance of the stationary distribution of states of multimode service policy networks

We consider open and closed preemptive-resume queueing systems with absolute priority of incoming customers. Single-server nodes have several service modes (regimes); the time of switching between the modes is exponential. Switching can be made to adjacent modes only. The amount of work required for servicing an incoming customer (workload) is a random variable with an arbitrary distribution function. For an open network, the input flow is Poissonian. We prove that the stationary distribution of the network states is invariant with respect to a functional form of workload distributions if the first moments are fixed.     

Queuing system with processor sharing and limited resources

Consideration was given to a processor-sharing system with heterogeneous customers serviced by system resources of two types: the first, discrete, type necessarily consists of an integer number N of units (servers), and the second type (memory) may be discrete or continuous. The customer type is defined by the number of units of the first-type resources required to service it. In addition to the need for the first-type resource, each customer is characterized by a certain volume, that is, the amount of the second-type resource required to service it. The total amount of customers (total busy resource of the second type) in the system is limited by a certain positive value (memory space) V. The customer volume and its length (amount of work required to service it) are generally dependent. Their joint distribution also depends on the customer type. For this system, the stationary distribution of the number of customers sojourning in the system and the probabilities of losing customers of each type were determined.     

A PSO-based intelligent service dispatching mechanism for customer expectation management

In the era of experience economy, service providers have to provide customers with high quality service experience in order to attract more customers and achieve higher customer satisfaction. Managing customer expectation is a critical approach for service providers to consider. Although customer expectation has been discussed across different research disciplines, to our knowledge, there is still no systematical and feasible way to apply customer expectation management into real environments. This study attempts to establish an intelligent service dispatching mechanism by using particle swarm optimization for customer expectation management. This mechanism can help service providers design and deliver satisfactory service experience to customers. In order to evaluate the effectiveness and robustness of this mechanism, this study employs micro- and macro-simulation experiments to confer and analyze its performance. The simulation results show service providers can gain benefit and raise customer satisfaction by managing customer expectation during service experience delivery. Meanwhile, customers can also receive memorable experiences and have positive responses to service providers and other customers. Consequently, a high performance ecosystem within service providers and customers can be formed.     

复杂客户网络拓扑性质研究

运用复杂网络的理论来研究客户网络的建立和发展复杂客户网络,通过对复杂客户网的小世界和无标度性质的分析来证实客户网络是一个复杂网络。并具备点分布、平均路径长度、聚集数等拓扑性质,研究结论对于企业赢得客户和保持客户规模具有指导意义。     

基于深度神经网络的电力客户诉求预判

电力企业的客户服务关系到客户的切身利益和企业的经营效益,提升客服系统对电力客户诉求预判的分析与理解能力是改善电力行业客服质量的重要途径之一。为高效、针对性地解决电力客户集中需求,做到“先于客户所想”,本文以深度神经网络技术为基础,针对电力领域改进传统的中文文本分词技术以及特征提取方法,给出电力客户诉求预判的方法和流程,并通过实验验证。本文提出的方法可快速精准地对电力客户服务工单文本进行分类,挖掘出隐藏的客户用电诉求,将服务由被动变主动,第一时间解决电力客户潜在诉求。     

A Single-Server Queueing System with Background Customers

A single-server queueing system with a Markov flow of primary customers and a flow of background customers from a bunker containing unbounded number of customers, i.e., the background customer flow is saturated, is studied. There is a buffer of finite capacity for primary customers. Service processes of primary as well as background customers are Markovian. Primary customers have a relative service priority over background customers, i.e., a background customer is taken for service only if the buffer is empty upon completion of service of a primary customer. A matrix algorithm for computing the stationary state probabilities of the system at arbitrary instants and at instants of arrival and completion of service of primary customers is obtained. Main stationary performance indexes of the system are derived. The Laplace—Stieltjes transform of the stationary waiting time distribution for primary customers is determined.__________Translated from Avtomatika i Telemekhanika, No. 6, 2005, pp. 74–88.Original Russian Text Copyright © 2005 by Bocharov, Shlumper.     

A Queueing Network with Random-Delay Signals

A queueing network with an input flow of signals, along with a flow of ordinary (positive) customers, at its nodes is studied. A random time is required to activate a signal upon arrival at a node. The stationary state probability distribution for a network with single-server nodes and exponential service time distribution is derived in product form. A product-form solution for a symmetric network with Markov service at nodes is also derived.     

Event-based optimization of admission control in open queueing networks

In this paper, we use the event-based optimization framework to study the admission control problem in an open Jackson network. The external arriving customers are controlled by an admission controller. The controller makes decision only at the epoch when an event of customer arrival happens. Every customer in the network obtains a fixed reward for each service completion and pays a cost with a fixed rate during its sojourn time (including waiting time and service time). The complete information of the system state is not available for the controller. The controller can observe only the number of total customers in the network. Based on the property of closed form solution of Jackson networks, we prove that the system performance is monotonic with respect to the admission probabilities and the optimal control policy has a threshold form. That is, when the number of total customers is smaller than a threshold, all of the arriving customers are admitted; otherwise, all are rejected. The sufficient condition and necessary condition of optimal policy are also derived. Furthermore, we develop an iterative algorithm to find the optimal policy. The algorithm can be executed based on a single sample path, which makes the algorithm online implementable. Simulation experiments are conducted to demonstrate the effectiveness of our approach.     

Product from solutions for multiserver centres with concurrent classes of customers

The MultiServer centre with Concurrent Classes of Customers (MSCCC) is a service centre consisting of B parallel identical exponential servers. The customers requesting service at the MSCCC centre belong to K groups. Customers arriving at the MSCCC centre are queued in the order of their arrival. A customer from group k will go into service at the MSCCC centre provided that one or more of the B servers is free and that at most n − 1 other group k customers are in service at the MSCCC centre.

The MSCCC centre can be applied to model systems where customers simultaneously occupy two resources. The system resources are partitioned into K primary and B secondary resources. A customer of group k can access primary resource k if it already is in possession of a secondary resource and if at most n − 1 other group k customers are using primary resource k.

This paper defines the MSCCC centre and presents several examples of computer (sub)systems that can be modelled using the MSCCC centre. The MSCCC centre is shown to satisfy local balance: therefore a multiclass queuing network consisting of BCMP and MSCCC centres has a product form solution. The joint probability distribution (JPD) for a queuing network consisting of several BCMP centres and one MSCCC centre is derived. Aggregation techniques are next used to reduce the JPD to a computationally tractable form. A Mean Value Analysis algorithm is presented for calculating the closed and open chain performance measures at the MSCCC centre.     

新颖的离散时间队列系统模型(英文)

带有正负顾客的连续时间单台服务器的队列系统得到了深入研究且已应用于多agent服务系统和计算机网络系统,而带有正负顾客的离散时间Geo/Geo/1队列研究在最近才出现。在拓展离散时间单台服务器Geo/Geo/1队列的基础上,提出了一个具有正负几何到达顾客的离散时间单台服务器GI/M/1队列模型,分析了队列静态长度分布和在RCH与RCE情况下的等待时间长度分布。     

FCM-based customer expectation-driven service dispatch system

Maintaining long-term customer loyalty has been an important issue in the service industry. Although customer satisfaction can be enhanced with better service quality, delivering appropriate services to customers poses challenges to service providers, particularly in real-time and resource-limited dynamic service contexts. However, customer expectation management has been regarded as an effective way for helping service providers achieve high customer satisfaction in the real world that is nevertheless less real-time and dynamic. This study designs a FCM-based customer expectation-driven service dispatch system to empower providers with the capability to deal effectively with the problem of delivering right services to right customers in right contexts. Our evaluation results show that service providers can make appropriate decisions on service dispatch for customers by effectively managing customer expectations and arranging their contextual limited resources and time via the proposed service dispatch system. Meanwhile, customers can receive suitable service and obtain high satisfaction when appropriate services are provided. Accordingly, a high-performance ecosystem can be established by both service providers and customers who co-create value in the dynamic service contexts.