On Admission Control Policy for Multi-tasking Live-chat Service Agents Research-in-progress Paper

Transcription

1 On Admission Control Policy for Multi-tasking Live-chat Service Agents Research-in-progress Paper

2 Paulo Goes Dept. of Management Information Systems Eller College of Management, The University of Arizona, Tucson, AZ Noyan Ilk Dept. of Management Information Systems Eller College of Management, The University of Arizona, Tucson, AZ J. Leon Zhao Dept. of Information Systems College of Business, City University of Hong Kong, Kowloon Tong, Hong Kong Abstract Many firms have adopted live-chat services on their websites to provide more intimate customer interactions. An important policy issue for managing the live-chat function is to determine the number of concurrent chat sessions handled by each live-chat service agent. Policies that incorporate information about the multi-tasking workload of a service agent may have direct impact on the overall agent performance. In this paper, we model a threshold type admission control policy to determine the optimal number of live-chat sessions per agent. Our analysis indicates that under increasing arrival rates, disabling the multi-tasking functionality may be more favorable in order to minimize the waiting times for preferred customers. In addition, we find out that the threshold level can affect the total revenue of the firm, even when the performance function is assumed to be a constant. 1. Introduction Live-chat is an online communication channel that is increasingly adopted by companies to provide customer services in online environments. Considered a synchronous (i.e. instantaneous) communication medium (Dennis et al. 2008; Froehle 2006), the strength of live-chat channel lies in its ability to support multiple customers with minimal service resources. A service agent using a live-chat system is expected to multi-task between several chat sessions concurrently, thereby increasing the overall productivity. Results supporting this argument have been presented in Shae et al. (2007), where it was observed that service agents could handle at least 3 chat sessions simultaneously without significant increase in average chat duration. In fact, many commercial live-chat systems allow service agents to multi-task 10 or more chat sessions, and this feature is promoted by their vendors as a unique strength of life-chat systems to maximize service productivity (Parature Inc. 2010). Unfortunately, the degree of productivity benefits gained from multi-tasking is subject to degradation over time and increasing workload (Iqbal and Horwitz 2007). Multi-tasking related events such as task-switching and work interruption have been shown to negatively affect the performance of a service agent. Psychology literature points out that loss of context associated with the task switch can be a major delay factor during the resumption (e.g. re-orientation) of the

3 initial task (Czerwinski et al. 2004). Mark et al. (2008) argue that workers try to compensate the loss of time due to interruptions by working faster, which comes at a price of increased stress and frustration. Along with increased multi-tasking workload, stress and frustration may result in cognitive overload of the server. When cognitive overload occurs, overall server performance diminishes due to attentional narrowing and working memory loss (Bekker and Borst 2006). This brief discussion, so far, points out that there exists a trade-off between productivity benefits and performance loss of service agents due to multi-tasking characteristic of live-chat systems. Information about the workload and the cognitive load of an agent is crucial to get the best performance from service agents. In this paper, we present an admission control model that considers such information to determine the optimal number of customers simultaneously served by a live-chat agent. Specifically, we consider threshold policies for a dynamic queue, where service times depend on the cognitive load of the agent that is affected by the number of jobs in service. Threshold policies are of our specific interest due to their ease of implementation in practice. Optimality of a threshold policy for single server, workload-dependent service time queue that assumes a concave service rate function was shown in Bekker and Borst (2006). Savla and Frazzoli (2010) prove a similar threshold policy to be optimal for homogeneous tasks with deterministic inter-arrival times. Our model differs from previous work on two aspects: (1) we consider a processor sharing discipline that divides the capacity of the server among all customers admitted into the service (therefore, enabling simultaneous live-chat sessions), and (2) we assume a two-class customer scheme with a preferred class for priority processing. Processor sharing discipline poses an interesting trade-off for the server. By increasing the admission level, more customers can be served simultaneously and in-queue waiting times can be decreased. However, this comes at the expense of increasing inservice waiting times. Considering the performance of the agent for a certain workload, the question then becomes how to find the optimal threshold level that would minimize the average waiting time in the system (i.e. queue plus service) and maximize the throughput. The two-class customer scheme adds another layer to this question by introducing priority processing for preferred customers. To study this issue, we model the live-chat system as a continuous time Markov process and analyze its steady-state behavior using numerical experiments. An intuitive expectation of this model is to see the best performance when the server performance level is at its highest. We present a case that contradicts this expectation under certain conditions. Our results indicate that when the arrival rates are increasing, switching the admission policy to no multi-tasking may provide better results, assuming that the firm is to minimize the average waiting time for its preferred customers. In a second case, we consider the agent performance to be constant regardless of the threshold level.

4 Under this condition, we find out that increasing the threshold level may be more favorable for certain situations, if the firm is to maximize its revenue. 2. Model We consider a single server queuing system (i.e., the live-chat agent in this study) with two classes of customers: H and L arriving to the system according to two independent Poisson processes with rates and, respectively. The service requirement a class customer is assumed to be exponentially distributed with mean, where. Each serviced class

5 customer brings in reward for the firm upon departure, assuming. Therefore, we consider H class customers as the preferred type for the firm. The server, at most, can process N number of customers simultaneously. The capacity of the system is also finite and an arriving customer is considered lost if there are C customers in the system (i.e. queue + service). The server works according to a processor sharing discipline and with the performance of, where denotes the total number of customers currently in service. is expected to follow the performance vs. workload model discussed in Cummings and Nehme (2010). Inspired by the well-known Yerkes-Dodson inverted-u relationship (Yerkes and Dodson 1908), this model states that the performance of a worker first increases and then decreases with increasing workload. We also assume complex task performance (i.e. H class) to get more severely affected under high levels of workload. After considering the impact of on service times, we define as the service rate of class. Finally, we assume that the server is work conserving (i.e. never idle when customers are waiting) and employs head-of-the-line priority processing, where class H customers have admission priority over class L customers, when both types are in queue. The system described above can be represented as a continuous time Markov chain with states, where and indicate the number of class H and class L customers in the system; and indicate the number of class H and class L customers in the service, respectively. Let S be the set of all feasible states, i.e.. For the ease of representation, we denote State as State, where. Transition rates for this Markov chain for the State can be given as follows; Table 1: Transition Rates for the Markov Chain and if and if if, if if, if 0 if if 0 if and 0 if

6 if and 0 if if if if if if if - if Note that the steady-state condition for this chain will always exist (regardless of condition) as the state space cannot grow beyond the system capacity. The vector

7 of the steady-state distribution can then be computed as the unique solution to the linear system, where is the transition-rate matrix, i.e.. Employing the normalization condition of, this system of linear equations can be solved by using Gaussian elimination. Solution of the steady-state distribution can then be used to obtain the following performance metrics: 2.1. Average Waiting Time in the System Average waiting time corresponds to the time a customer of class u ( ) spends in the system (queue + service) before his/her departure. By applying Little s Law, we can define the average waiting times for both classes as following: (1) 2.2. Long-run Average Throughput and Total Expected Revenue Denote is the long-run average throughput for class customers. Using steady-state distributions, can be calculated as; (2) If the firm s objective is to maximize its total revenue (i.e. the sum of rewards gained by processing customers), it needs to consider both the throughput and the reward rate per customer class. Since a reward is only obtained upon the departure of a customer, we can define the expected total revenue based on throughput as following; (3) 3. Numerical Experiments: In this section, we present two cases to discuss insights for developing an admission control policy. In the first case, we study the impact of admission threshold level on average waiting time of H class customers under varying arrival rates. In the second case, we consider that the firm s objective is to maximize the total expected revenue and analyze how the threshold level affects this objective. The first case considers server performance as a function of the workload, whereas the second case assumes it to be constant. For revenue formulation, we set the base case reward rates as $100 and $50 per customer for each class, respectively. The capacity of the system is set at maximum 10 customers Case I: Impact of Admission Threshold (N) on Average Waiting Time In this case, the firm wants to find the optimal admission threshold level to minimize the average waiting times for H class customers. We set the base case values as following:

8 . We assume to be an increasing and then decreasing function that achieves its global maximum at for both classes. Table 2 shows the waiting times for H under different threshold rates and increasing customer arrival rates. The shaded area shows the threshold level, when the server performance reaches the maximum. We observe that as the arrivals to the system increase, optimal threshold level moves away from global maximum of the server performance and settles at no multi-tasking. A possible explanation of this result is that with increasing customer arrival rates, the system gets flooded with L class customers (i.e. non preferred customers). When the admission level is high, majority of the customers in service would be L class, therefore slowing down the H class service rate. On the other hand, when only one customer is admitted in service at a time, H class customers are guaranteed to wait for one customer, at most, since any H customer in queue will jump in front of the queue due to the head-of-the-line processing discipline. Table 2: Average Waiting Time per H class under Different Thresholds and Arrival Rates,,,,, Threshold Avg. time 3.2. Case II: Impact of Admission Threshold (N) on Total Expected Revenue In the second case, we assume the server performance function to be a constant, meaning that it is not affected by the changing workload. An initial expectation for such a condition would be that, admission threshold has no impact on the steady-state throughput and the total expected revenue. Figure 1 shows results from certain given conditions that contradict this expectation. While keeping the overall utilization the same, we can see that at high service rate levels for L class customers, the revenues may increase as the threshold level increases. This result can be explained by considering the capacity restriction of the system. When more customers can be admitted at the same time, the system will less likely to grow to the capacity limit and will have less probability of blocking future arrivals. Therefore, the net throughput in this condition will be higher. Threshold Avg. time

9 Threshold Threshold Threshold Avg. time Avg. time Avg. time

10 Figure 1. Threshold vs. Total Revenue for Different Rate Parameters 4. Conclusion In this study, we considered the problem of admission control for live-chat systems that support multi-tasking functionality. Multi-tasking enables live-chat service agents to interact with more than one customer at the same time. While this condition has the potential to increase overall service productivity, it also brings the possibility of overloading cognitive capacity of the server. Our goal has been to model this trade-off to determine the optimal number of customers to be simultaneously served by a livechat service agent. In our model, we considered: (1) a processor sharing discipline with state dependent service times based on the workload, and (2) a priority processing scheme that assigns admission priority to preferred customers of the system. Our numerical experiments pointed out counter-intuitive results that may have policy making implications. First of all, we found out that the global maximum of the cognitive performance function needs not always be the optimal threshold policy to minimize the average waiting time for preferred customers. Under increasing arrival rates, no multitasking may achieve better results. Second, we observed that even when the performance function is assumed to be a constant, admission threshold may still have an impact on the total revenues of the firm. This work-in-progress research is being improved on multiple levels. Our interim goal is to relax the equal capacity allocation assumption for processor sharing. In addition, we plan to study different queueing disciplines for the system and extend the analysis to additional performance metrics such as in-queue waiting times. References Dennis, A.R., Fuller, R.M. and Valacich, J.S. Media, Tasks, and Communication Processes: A Theory of Media Synchronicity, MIS Quarterly (32:3), 2008, pp Froehle, C. M. Service Personnel, Technology, and Their Interaction in Influencing Customer Satisfaction, Decision Sciences (37:1), 2006, pp Shae, Z-Y., Garg, D., Bhose, R., Mukherjee, R., Guven, S. and Pingali, G. Efficient Internet Chat Services for Help Desk Agents, in Preceedings of the International Conference on Services Computing, Total Revenue Y Threshold Level

11 Parature Inc., The Advantages of Using Live Chat in Your Customer Service Organization, White Paper, Retrieved from: Iqbal, S. T. and Horvitz, E. Disruption and Recovery of Computing Tasks: Field Study, Analysis and Directions, in Proceedings of the ACM Conference on Human Factors in Computing Systems (CHI), Mark, G., Gudith, D. and Klocke, U., The Cost of Interrupted Work: More Speed and Stress, in Proceedings of the ACM Conference on Human Factors in Computing Systems (CHI), Czerwinski, M., Horvitz, E., and Wilhite, S., A Diary Study of Task Switching and Interruptions, in Proc. of the ACM Conf. on Human Factors in Computing Systems (CHI), Bekker, R., and Borst, S. C., Optimal Admission Control in Queues with Workloaddependent Service Rates, Probability in Engineering and Informational Sciences (20), 2006, pp Savla, K. and Frazzoli, E., A Dynamical Queue Approach to Intelligent Task Management for Human Operators, in Proceedings of the IEEE (to appear), Cummings, M. L. and Nehme, C. E., Modeling the impact of workload in network centric supervisory control settings. in Neurocognitive and Physiological Factors During High-Tempo Operations, pp , Surrey, UK: Ashgate, Yerkes, R. M., and Dodson, J. D., The relation of strength of stimulus to rapidity of habitformation, Journal of Comparative Neurology and Psychology, (18), 1908, pp