Performance and Cost Analysis of Multi-Server Queues with Backup Servers under Server Failures

This study examines a multi-server tandem queueing system that is plagued by service disruptions from server failures and low service rates—problems that have a tendency to cause customer dissatisfaction, system delay, and abandonment. To counteract these impacts, we introduce an intelligent service continuity model with a backup server in case of primary server failures. Recognizing the cost-ineffectiveness of backup server activation for small queue sizes, the paper provides a strategic activation policy based on queue length, customer abandonment rate, and repair time. System dynamics are represented by a multi-dimensional continuous-time Markov process, which provides transient and steady-state behavior analysis. The model extends classical queuing systems by introducing Phase-Type (PH) distributions for the service and Markov Arrival Processes (MAPs) for accommodating correlated arrivals and sophisticated service behavior. There is not much in the literature that suggests extensive work has been done on tandem networks of such advanced stochastic modeling; Chakravarthy et al., Klimenok et al., and Dudin et al. have already developed basic methods, which are extended in the present work. Decision-theoretic techniques and cost-minimization functions are employed to determine optimal operating policies. Numerical experiments show the efficiency of employing strategic backup server operation in significantly reducing expected operational cost without compromising service quality, rendering the model a robust one for real-time mission-critical service systems