Fluid Approximation of a Call Center Model with Redials and Reconnects

In many call centers, callers may call multiple times. Some of the calls are re-attempts after abandonments (redials), and some are re-attempts after connected calls (reconnects). The combination of redials and reconnects has not been considered when making staffing decisions, while ignoring them will inevitably lead to under- or overestimation of call volumes, which results in improper and hence costly staffing decisions. Motivated by this, in this paper we study call centers where customers can abandon, and abandoned customers may redial, and when a customer finishes his conversation with an agent, he may reconnect. We use a fluid model to derive first order approximations for the number of customers in the redial and reconnect orbits in the heavy traffic. We show that the fluid limit of such a model is the unique solution to a system of three differential equations. Furthermore, we use the fluid limit to calculate the expected total arrival rate, which is then given as an input to the Erlang A model for the purpose of calculating service levels and abandonment rates. The performance of such a procedure is validated in the case of single intervals as well as multiple intervals with changing parameters

BRAVO for many-server QED systems with finite buffers

This paper demonstrates the occurrence of the feature called BRAVO (Balancing Reduces Asymptotic Variance of Output) for the departure process of a finite-buffer Markovian many-server system in the QED (Quality and Efficiency-Driven) heavy-traffic regime. The results are based on evaluating the limit of a formula for the asymptotic variance of death counts in finite birth--death processes

Sistem Penyusunan Kepegawaian Pada Manajemen Call Center Dengan Multi-class Pelanggan Dan Multi-pool Server

Penelitian ini mempertimbangkan suatu model call center dari pengarahan berbasis ketrampilan. Model ini merupakan server yang bersifat homogen dan heterogen dengan sejumlah aliran masuk dan sejumlah kelompok agen, dengan tingkat kedatangan seketika yang diperbolehkan bersifat tergantung dengan waktu (time-dependent) dan bersifat stokastik. Pelanggan yang tidak sabar menunggu untuk dilayani agen kemungkinan akan meninggalkan antrian dan terdapat biaya hukuman yang berhubungan dengan penundaan tersebut. Metoda penyusunan kepegawaian yang diajukan mengoptimalkan perimbangan antara biaya personel dan hukuman penundaan dengan melakukan pengembangan dan penjelasan suatu metoda praktis untuk mengukur jumlah kelompok agen. Dengan menggunakan suatu model stokastik fluida, metoda ini mereduksi permasalahan dalam penyusunan kepegawaian ke bentuk newsvendor problem, yang dapat dipecahkan secara numerik melalui suatu kombinasi linear programming dan simulasi Monte Carlo. Hasil penelitian dan analisa yang diperoleh, dimana dalam semua kasus untuk ukuran kelompok yang diperoleh dari hasil simulasi hampir mendekati optimal dengan hasil dari metode pendekatan yang diusulkan, sekitar 2%-3%.

Optimisation of stochastic networks with blocking: a functional-form approach

This paper introduces a class of stochastic networks with blocking, motivated by applications arising in cellular network planning, mobile cloud computing, and spare parts supply chains. Blocking results in lost revenue due to customers or jobs being permanently removed from the system. We are interested in striking a balance between mitigating blocking by increasing service capacity, and maintaining low costs for service capacity. This problem is further complicated by the stochastic nature of the system. Owing to the complexity of the system there are no analytical results available that formulate and solve the relevant optimization problem in closed form. Traditional simulation-based methods may work well for small instances, but the associated computational costs are prohibitive for networks of realistic size. We propose a hybrid functional-form based approach for finding the optimal resource allocation, combining the speed of an analytical approach with the accuracy of simulation-based optimisation. The key insight is to replace the computationally expensive gradient estimation in simulation optimisation with a closed-form analytical approximation that is calibrated using a single simulation run. We develop two implementations of this approach and conduct extensive computational experiments on complex examples to show that it is capable of substantially improving system performance. We also provide evidence that our approach has substantially lower computational costs compared to stochastic approximation