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Construction and analysis of a generalized contact center model
Abstract
We construct and study a model of arrival and servicing of calls in modern contact centers. The model takes into account that servicing staff divides into operators and consultants, that a call can be repeated if all operators, consultants, or access lines are busy, and also due to an unsuccessful end of waiting time, and the presence of voice answering machines. We define characteristics of call servicing, consider a method for computing them based on constructing and solving a system of statistical equilibrium equations. We propose a procedure to estimate the intensity of primary calls arrival based on measurements of general characteristics of call servicing in the contact center. We consider specific features of planning for the number of operators and access lines.
... Just like in [6], the transmission rate is controllable, but now the model has a mechanism for resending lost packets. QS models with retrials are relevant when modeling the work of contact centers, where customer calls can be repeated due to busy operators or due to the end of waiting time [21]. In the model under consideration, we distinguish two performance indices for optimizing the system operation: the time of successfully sending out a packet and the amount of resources used. ...
... Now we can describe a way to solve the problem (21). ...
... The strategy μ * , defined in (24) at ν = ν * is the steady-state optimal control in the problem of minimizing the extended functional (21), with L[μ * , λ] = ν * . ...
We consider a closed network consisting of two queuing systems: the main system simulates a packet transmission queue over an unreliable communication channel, and the auxiliary multiserver system contains lost packets for resending. The service rate in the main system is controllable and is supposed to be optimized with the aim of minimizing the time of successful transmission, taking into account the cost of using network resources. We obtain optimality conditions in two cases: 1) in the model based on fluid approximation in the presence of heavy load; 2) in the steady state using stationary strategies.
... An excellent description of call centers and general issues in applying queueing models to studies were presented in [1]; some other general issues on the topic may be found in [2][3][4][5]. In this paper, we consider a call center model in the form of a multi-server queue with an incoming Poisson flow of calls, recurrent service, and an unlimited number of waiting places (M/G/N). ...
The paper considers the model of a call center in the form of a multi-server queueing system with Poisson arrivals and an unlimited waiting area. In the model under consideration, incoming calls do not differ in terms of service conditions, requested service, and interarrival periods. It is assumed that an incoming call can use any free server and they are all identical in terms of capabilities and quality. The goal problem is to find the stationary distribution of the number of calls in the system for an arbitrary recurrent service. This will allow us to evaluate the performance measures of such systems and solve various optimization problems for them. Considering models with non-exponential service times provides solutions for a wide class of mathematical models, making the results more adequate for real call centers. The solution is based on the approximation of the given distribution function of the service time by the hyperexponential distribution function. Therefore, first, the problem of studying a system with hyperexponential service is solved using the matrix-geometric method. Further, on the basis of this result, an approximation of the stationary distribution of the number of calls in a multi-server system with an arbitrary distribution function of the service time is constructed. Various issues in the application of this approximation are considered, and its accuracy is analyzed based on comparison with the known analytical result for a particular case, as well as with the results of the simulation.
A mathematical model of a fully accessible communication system has been constructed and investigated, taking into account the repetition of a call after the preliminary service stage and due to the busy service devices. The probability of call retry depends on the stage of the connection establishment at which the denial of service was received. The model also assumes that the user’s stay in the call repetition state is limited by a random variable that has an exponential distribution, which determines the aging time of the transmitted information. It is shown that the exact values of the stationary characteristics of the constructed model can be calculated by an efficient recursive algorithm developed for the model where the user repeats the call only because the service devices are busy. The constructed model and methods of its analysis can be used for evaluation of the positive effect that the use of the preliminary service like chatbot creates when planning the required number of call center operators. The model also makes it possible to estimate the share of incoming requests that need to be redirected to other call centers in an overload situation. Numerical examples are given to illustrate the practical use of the results obtained.
In this paper, we consider the LoRa technology to expand sensor network coverage in smart sustainable cities. A model of a LoRa mesh network is proposed using the AODV protocol in packet routing. With a simulation model developed based on OMNET++, a series of computer experiments was carried out with changing various parameters. In the experiments results, the end-to-end delay and packet loss ratio were analyzed in the dependence on the number of nodes and packet size in the network. The simulation results show that the latency is relatively high in the LoRa mesh network, but it might be accepted for some applications.
The mathematical model of public-safety answering points (PSAP) functioning is constructed and analyzed. In the model the usage of interactive voice response (IVR) and the possibility of call repetition in case of blocking or unsuccessful waiting are taken into account. Algorithm of characteristics estimation based on truncation of used infinite space of states and solving the system of state equations is suggested. Relative error of characteristics calculation caused by truncation is found. The first two or three terms in the asymptotic expansion of basic stationary performance measures into a power series of the intensity of primary calls as it tends to infinity are derived. Approximate algorithm of performance measures estimation is constructed. The usage of the model for elimination of negative effects of PSAP overload is considered.
In this work we provide an analysis of Internet of Things concept and the Tactile Internet, as well as trends in traffic served by communication networks, build a real time interactive system between the human and the machine and introduce a new evolution in human-machine (H2M) communication. The most important challenge in realizing Tactile Internet is the latency requirement. In this paper we consider the impact of Internet of Things and tactile internet traffic, formed by monitoring and dispatching control systems or other systems, when the properties of this traffic are described by regular data stream properties. We estimate the impact of this traffic on such key QoS indicators as data delivery delay and probability of loss. As a model of a communication network, we consider a queuing system (QS) with a combined service discipline.
The mathematical model of call center functioning in case of overload is constructed and analyzed. In the model multi-skilled routing based on usage of one group of operators capable of serving simple requests and several groups of experts (consultants) handling more advanced topics is taken into account together with the possibility of request repetition in case of blocking or unsuccessful waiting time. Markov process that describes model functioning is constructed. Main performance measures of interest are defined through the values of stationary probabilities of model’s states. Algorithm of characteristics estimation is suggested based on solving the system of state equations. Expressions that relates introduced performance measures in form of conservation laws are derived. It is shown how to use found relations for quantitative and qualitative analysis of the model functioning. The usage of the model for elimination of call center overload based on reducing of the input flow is considered.
The data transmission process is modelled by a Markov closed queuing network, which consists of two stations. The primary station describes the process of sending packets over a lossy channel by means of a finite and single-channel queue. The auxiliary station, being a multichannel queuing system, accumulates packets lost by the primary station and forwards them back for retrial. The transmission rate at the primary station and the retrial rate at the auxiliary station are in the specified ranges and are subject to optimization in order to minimize the time of successful delivery and the amount of network resources used. The explicit expressions for these characteristics are derived in the steady-state mode in order to formulate the problem of bi-criterion optimization. The optimal policies are established in two scenarios: the first problem is to minimize the average time of successful transmission with limited resources; the second problem is to minimize the consumption of network resources under the constraint on the time for successful transmission. The set of Pareto-optimal policies is obtained by solving the problem of minimization of the augmented functional. The quality characteristics of approximate solutions that do not take into account the service rate in the auxiliary system are analyzed.
We continue the study of a generalized call center model presented in [1]. The model takes into account the following characteristic features of reference and information services: division of the servicing personnel into operators and consultants; the possibility of repeating a claim when operators, consultants, or access lines are busy, or due to a failed end of waiting time; the presence of automatic responding machines. For the considered model, we construct approximate algorithms for estimating stationary characteristics of servicing incoming claims. The algorithms are based on using special cases of the model in question, on applying asymptotic decompositions of characteristics as the repetition intensity tends to zero, and on implementing the model decomposition principle into individual segments with specially tuned values of input parameters. We show numerical examples that illustrate the errors of the resulting computational procedures.
Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments traditional operational models are of great value—and at the same time fundamentally limited—in their ability to characterize system performance.
We review the state of research on telephone call centers. We begin with a tutorial on how call centers function and proceed to survey academic research devoted to the management of their operations. We then outline important problems that have not been addressed and identify promising directions for future research.
A Call center may be defined as a service unit where a group of agents handle a large volume of incoming telephone calls for the purpose of sales, service, or other specialized transactions. Typically a call center consists of telephone trunk lines, a switching machine known as the automatic call distributor (ACD) together with a voice response unit (VRU), and telephone sales agents. Customers usually dial a special number provided by the call center; if a trunk line is free, the customer seizes it, otherwise the call is lost. Once the trunk line is seized, the caller is instructed to choose among several options provided by the call center via VRU. After completing the instructions at the VRU, the call is routed to an available agent. If all agents are busy, the call is queued at the ACD until one is free. One of the challenging issues in the design of a call center is the determination of the number of trunk lines and agents required for a given call load and a given service level. Call center industries use the Erlang-C and the Erlang-B formulae in isolation to determine the number of agents and the number of trunk lines needed respectively.
In this paper we propose and analyze a flow controlled network model to capture the role of the VRU as well as the agents. Initially, we assume Poisson arrivals, exponential processing time at the VRU and exponential talk time. This model provides a way to determine the number of trunk lines and agents required simultaneously. An alternative simplified model (that ignores the role of the VRU) will be to use anM|M|S|N queueing model (whereS is the number of agents andN is the number of trunk lines) to determine the optimalS andN subject to service level constraints. We will compare the effectiveness of this simplified model and other approximate methods with our model. We will also point out the drawbacks of using Erlang-C and Erlang-B formulae in isolation.
Chislennye metody rascheta sistem s povtornymi vyzovami (Numerical Methods for Analysis of Systems with Repeated Calls)
- S N Stepanov
- SN Stepanov
Modeling the Flows of Incoming and Serviced Calls in City Information Services, Elektrosvyaz
- S N Stepanov
- L G Ukhlovskaya
- SN Stepanov