基于耐心阈值下联络中心放弃率的仿真研究

顾客放弃率是衡量联络中心服务水平的一项重要指标.传统呼叫中心的顾客遵循先到先服务的原则,但考虑到顾客的耐心程度,会有部分顾客在排队过程中流失.通过设置顾客时耐心阈值并考虑为会员顾客增加特定的座席渠道,或在原有的人力下调整座席渠道数量,在传统呼叫中心模型的基础上建立新型的联络中心排队模型.运用ProModel仿真软件对顾...     

Analysis of a continuous time SM[K]/PH[K]/1/FCFS queue: Age process, sojourn times, and queue lengths

This paper studies a continuous time queueing system with multiple types of customers and a first-come-first-served service discipline.Customers arrive according to a semi-Markov arrival process and the service times of individual types of customers have PH-distributions.A GI/M/1 type Markov process for a generalized age process of batches of customers is constructed.The stationary distribution of the GI/M/1 type Markov process is found explicitly and,consequently,the distributions of the age of the batch in service,the total workload in the system,waiting times,and sojourn times of different batches and different types of customers are obtained.The paper gives the matrix representations of the PH-distributions of waiting times and sojourn times.Some results are obtained for the distributions of queue lengths at departure epochs and at an arbitrary time.These results can be used to analyze not only the queue length,but also the composition of the queue.Computational methods are developed for calculating steady state distributions related to the queue lengths,sojourn times,and waiting times.     

A batch arrival retrial queue with starting failures,feedback and admission control

This paper is concerned with the analysis of a feedback M^[X]/G/1 retrial queue with starting failures and general retrial times. In a batch, each individual customer is subject to a control admission policy upon arrival. If the server is idle, one of the customers admitted to the system may start its service and the rest joins the retrial group, whereas all the admitted customers go to the retrial group when the server is unavailable upon arrival. An arriving customer (primary or retrial) must turn-on the server, which takes negligible time. If the server is started successfully (with a certain probability), the customer gets service immediately. Otherwise, the repair for the server commences immediately and the customer must leave for the orbit and make a retrial at a later time. It is assumed that the customers who find the server unavailable are queued in the orbit in accordance with an FCFS discipline and only the customer at the head of the queue is allowed for access to the server. The Markov chain underlying the considered queueing system is studied and the necessary and sufficient condition for the system to be stable is presented. Explicit formulae for the stationary distribution and some performance measures of the system in steady-state are obtained. Finally, some numerical examples are presented to illustrate the influence of the parameters on several performance characteristics.     

Strong approximation method and the (functional) law of iterated logarithm for <Emphasis Type="Italic">GI</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/1 queue

In this paper, a unified method based on the strong approximation (SA) of renewal process (RP) is developed for the law of the iterated logarithm (LIL) and the functional LIL (FLIL), which quantify the magnitude of the asymptotic rate of the increasing variability around the mean value of the RP in numerical and functional forms respectively. For the GI/G/1 queue, the method provides a complete analysis for both the LIL and the FLIL limits for four performance functions: The queue length, workload, busy time and idle time processes, covering three regimes divided by the traffic intensity.     

THE M/M/c QUEUE WITH （e,d） SETUP TIME

The authors present a new queueing model with （e, d） setup time. Using the quasi-birth-and-death process and matrix-geometric method, the authors obtain the stationary distribution of queue length and the LST of waiting time of a customer in the system. Furthermore, the conditional stochastic decomposition results of queue length and waiting time are given.     

A perishable inventory system with service facilities, <Emphasis Type="Italic">MAP</Emphasis> arrivals and <Emphasis Type="Italic">PH</Emphasis> — Service times

We consider a continuous review perishable （s,S） inventory system with a service facility consisting of a waiting hall of finite capacity and a single server. We assume two types of customers, ordinary and negative, arrive according to a Markovian Arrival Process （MAP）. An ordinary customer joins the queue and a negative customer instead of joining the queue removes one ordinary customer from the queue. The removal rule adopted in this paper is RCE （removal of a customer from the end）. The individual customer＇s unit demand is satisfied after a random time of service which is assumed to have a phase-type distribution. The life time of each item and the lead time of the reorders have been assumed to be independent exponential distributions. The joint probability distribution of the number of customers in the system and the inventory level is obtained for the steady state case. Various stationary system performance measures are computed and the total expected cost rate is calculated. The results are illustrated numerically.     

A discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times

The authors discuss a discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times. As soon as the orbit is empty, the server takes a vacation. However, the server is allowed to take a maximum number J of vacations, if the system remains empty after the end of a vacation. If there is at least one customer in the orbit at the end of a vacation, the server begins to serve the new arrivals or the arriving customers from the orbit. For this model, the authors focus on the steady-state analysis for the considered queueing system. Firstly, the authors obtain the generating functions of the number of customers in the orbit and in the system. Then, the authors obtain the closed-form expressions of some performance measures of the system and also give a stochastic decomposition result for the system size. Besides, the relationship between this discrete-time model and the corresponding continuous-time model is also investigated. Finally, some numerical results are provided.     

PHASE TRANSITION IN SEQUENCE UNIQUE RECONSTRUCTION

In this paper, sequence unique reconstruction refers to the property that a sequence is uniquely reconstructable from all its K-tuples. We propose and study the phase transition behavior of the probability P（K） of unique reconstruction with regard to tuple size K in random sequences （iid model）. Based on Monte Carlo experiments, artificial proteins generated from lid model exhibit a phase transition when P（K） abruptly jumps from a low value phase （e.g. 〈 0.1） to a high value phase （e.g. 〉 0.9）. With a generalization to any alphabet, we prove that for a random sequence of length L, as L is large enough, P（K） undergoes a sharp phase transition when p ≤ 0.1015 where p = P （two random letters match）. Besides, formulas are derived to estimate the transition points, which may be of practical use in sequencing DNA by hybridization. Concluded from our study, most proteins do not deviate greatly from random sequences in the sense of sequence unique reconstruction, while there are some ＂stubborn＂ proteins which only become uniquely reconstructable at a very large K and probably have biological implications.     

An M/M/1 Queueing-Inventory System with Geometric Batch Demands and Lost Sales

This paper studies an M/M/1 queueing-inventory system with batch demands. Customers arrive in the system according to a compound Poisson process, where the size of the batch demands for each arrival is a random variable that follows a geometric distribution. The inventory is replenished according to the standard (s,S) policy. The replenishment time follows an exponential distribution. Two models are considered. In the first model, if the on-hand inventory is less than the size of the batch demands of an arrived customer, the customer takes away all the items in the inventory, and a part of the customer’s batch demands is lost. In the second model, if the on-hand inventory is less than the size of the batch demands of an arrived customer, the customer leaves without taking any item from the inventory, and all of the customer’s batch demands are lost. For these two models, the authors derive the stationary conditions of the system. Then, the authors derive the stationary distributions of the product-form of the joint queue length and the on-hand inventory process. Besides this, the authors obtain some important performance measures and the average cost functions by using these stationary distributions. The results are illustrated by numerical examples.     

The recursive solution of queue length for <Emphasis Type="Italic">Geo/G</Emphasis>/1 queue with <Emphasis Type="Italic">N</Emphasis>-policy

This paper considers a discrete-time queue with N-policy and LAS-DA(late arrival system with delayed access) discipline.By using renewal process theory and probability decomposition techniques,the authors derive the recursive expressions of the queue-length distributions at epochs n~-,n~+,and n.Furthermore,the authors obtain the stochastic decomposition of the queue length and the relations between the equilibrium distributions of the queue length at different epochs(n~-,n~+,n and departure epoch D_n).     

Transient Queue Size Distribution Solution of Geom / G / 1 Queue with Feedback-A Recursive Method

This paper considers the Geom / G / 1 queueing model with feedback according to a late arrival system with delayed access (LASDA). Using recursive method, this paper studies the transient property of the queue size from the initial state N(0⁺) = i. Some new results about the recursive expression of the transient queue size distribution at any epoch n ⁺ and the recursive formulae of the equilibrium distribution are obtained. Furthermore, the recursive formulae of the equilibrium queue size distribution at epoch n ⁻, and n are obtained, too. The important relations between stationary queue size distributions at different epochs are discovered (being different from the relations given in M / G / 1 queueing system). The model discussed in this paper can be widely applied in all kinds of communications and computer network. This research is supported by the National Natural Science Foundation of China under Grant No. 70871084, the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 200806360001, and the Scientific Research Fund of Southwestern University of Finance and Economics.     

A single server retrial queue with general retrial times and two-phase service

An M / G / 1 retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated in this paper. Customers are allowed to balk and renege at particular times. Assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS discipline. All customers demand the first “essential” service, whereas only some of them demand the second “optional” service, and the second service is multioptional. During the service, the server is subject to breakdown and repair. Assume that the retrial time, the service time, and the repair time of the server are all arbitrarily distributed. By using the supplementary variables method, the authors obtain the steady-state solutions for both queueing and reliability measures of interest. This research is supported by the National Natural Science Foundation of China under Grant No. 10871020.     

The bulk input M[X] /M/1 queue with working vacations

In this paper, we analyze a bulk input M^[X] /M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matrix analysis method, highly complicated probability generating function(PGF) of the stationary queue length is firstly derived, from which we got the stochastic decomposition result for the stationary queue length which indicates the evident relationship with that of the classical M^[X] /M/1 queue without vacation. It is important that we find the upper and the lower bounds of the stationary waiting time in the Laplace transform order using the properties of the conditional Erlang distribution. Furthermore, we gain the mean queue length and the upper and the lower bounds of the mean waiting time.     

Queue size distribution of Geo/G/1 queue under the Min(<Emphasis Type="Italic">N,D</Emphasis>)-policy

This paper considers a discrete-time Geo/G/1 queue under the Min(N,D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first (Min(N,D)-policy). By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of the transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n ⁺. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution. Furthermore, the important relations between the steady state queue length distributions at different time epochs n ^-, n and n ⁺ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.     

ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS II： M（n）/G/1/K

We study a single-server queueing system with state-dependent arrivals and general service distribution, or simply M（n）/G/1/K, where the server follows an N policy and takes multiple vacations when the system is empty. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirements are the Laplace-Stieltjes transforms of the service time distribution and the vacation time distribution, and the state-dependent arrival rate. The computational complexity of the algorithm is O（K^3）.     

Discrete-time Geo/G/1 retrial queues with general retrial time and Bernoulli vacation

This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy.It is assumed that the server, after each service completion,begins a process of search in order to find the following customer to be served with a certain probability,or begins a single vacation process with complementary probability. This paper analyzes the Markov chain underlying the queueing system and obtain its ergodicity condition.The generating functions of the number of customers in the orbit and in the system are also obtained along with the marginal distributions of the orbit size when the server is idle,busy or on vacation.Finally,the author gives two stochastic decomposition laws,and as an application the author gives bounds for the proximity between the system size distributions of the model and the corresponding model without retrials.     

CUSTOMER EQUITY： MAKING MARKETING STRATEGY FINANCIALLY ACCOUNTABLE

1. Introduction The long-term value of a firm is largelydetermined by the value of the company’scustomer relationships, which result in thefirm’s ‘customer equity’ (Blattberg andDeighton 1996), defined by Rust, Lemon andZeithaml (2000, p.4…     

Scheduling problems — An overview

There seems to be a significant gap between the theoretical and the practical aspects ofscheduling problems in the job shop environment. Theoretically, scheduling systems are designed onthe basis of an optimum approach to the scheduling model. However in the practice, the optimum thatis built into the scheduling applications seems to face some challenges when dealing with the dynamiccharacter of a scheduling system, for instance machine breakdown or change of orders. Schedulingsystems have become quite complex in the past few years. Competitive business environments andshorter product life cycles are the imminent challenges being faced by many companies these days.These challenges push companies to anticipate a demand driven supply chain in their businessenvironment. A demand-driven supply chain incorporates the customer view into the supply chainprocesses. As a consequence of this, scheduling as a core process of the demand-driven supply chainmust also reflect the customer view. In addition, other approaches to solving scheduling problems, forinstance approaches based on human factors, prefer the scheduling system to be more flexible in bothdesign and implementation. After discussion of these factors, the authors propose the integration of adifferent set of criteria for the development of“ scheduling systems which not only appears to have abetter flexibility but also increased customer-focus.     

New Results on H∞ Control for Nonlinear Conformable Fractional Order Systems

This paper deals with H_∞ control problem for nonlinear conformable fractional order systems. The authors first derive new sufficient condition for exponential stability of nonlinear conformable fractional order systems based on Lyapunov-like function method for conformable fractional order systems and linear matrix inequalities(LMIs) approach. Then, by introducing a new concepts of H_∞ control problem for nonlinear conformable fractional order systems, the authors study H_∞ performance analysis and H_∞ state feedback controller design problems for the considered systems. In terms of LMIs, a sufficient condition is proposed to ensure the nonlinear conformable fractional order systems are not only exponentially stable, but also satisfy H_∞ performance γ. An explicit expression for state feedback controllers is also designed to make the closed-loop system is exponentially stable with H_∞performance γ. Finally, numerical examples are given to illustrate the validity and effectiveness of the proposed results.     

H ∞ control of networked multi-agent systems

This paper concerns the disturbance rejection problem arising in the coordination control of a group of autonomous agents subject to external disturbances. The agent network is said to possess a desired level of disturbance rejection, if the H _∞ norm of its transfer function matrix from the disturbance to the controlled output is satisfactorily small. Undirected graph is used to represent the information flow topology among agents. It is shown that the disturbance rejection problem of an agent network can be solved by analyzing the H _∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. An interesting result is that the disturbance rejection ability of the whole agent network coupled via feedback of merely relative measurements between agents will never be better than that of an isolated agent. To improve this, local feedback injections are applied to a small fraction of the agents in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. Finally, extensions to the case when communication time delays exist are also discussed. This research is supported by the Natural Science Foundation of China under Grants Nos. 10832006 and 60674093.