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We investigate a system with two types of customers wherein each customer type has a dedicated server. When the corresponding dedicated server is busy, we allow customer overflow to the non-dedicated server, and the service time of each server is customer-dependent. The objective of this study is to assess the negative consequences of overflow. On the basis of the analytical stationary distribution of the proposed two-server model, we first identify the conditions under which overflow leads to improvement of throughputs. Second, we obtain customers' overflow rates and ratios. For a symmetric system under heavy traffic, the wrong assignment ratio comes close to 50%. Third, we analyze the probability that a customer is served by a non-dedicated server. The probability that both servers are serving non-dedicated customers approaches 25% in a symmetric system under heavy traffic. Finally, we determine various overflow conditions while including the overflow costs. [ABSTRACT FROM AUTHOR]

Chaining configurations (e.g. 2-chain) have been widely applied in service systems to improve responsiveness to customer demand. In this paper, we propose an approximation method for the analysis of symmetric parallel queueing systems with 2-chain configuration and preemptive priority. In the queueing system of interest, the arrival processes of different types of customers follow independent Poisson processes with identical arrival rate λ, and service times of different types of customers are exponentially distributed with identical service rate μ. Each server serves its primary customers with preemptive priority. When there are no primary customers in the system, the server serves secondary customers. We first derive the system stability condition. Then, we analyse the system's various performance measures. Our approach relies on the matrix-analytic method coupled with the idle probability of each server, which is proved to be. The average queue length of each queue and the rate that each server serves its secondary customers (i.e. the helping rate) can be estimated using our proposed method. Finally, we conduct numerical studies to demonstrate the accuracy of our proposed approximation method. [ABSTRACT FROM AUTHOR]

In this paper, we study the performance of service systems with priority upgrades. We model the service system as a single-server two-class priority queue, with queue 1 as the normal queue and queue 2 as the priority queue. The queueing model of interest has various applications in healthcare services, perishable inventory and project management. We comprehensively examine the system's stationary distribution, computational algorithm design and sensitivity analysis. We observe that when queue 2 is large, the conditional distribution of queue 1 approximates a Poisson distribution. The tail probability of queue 2 decays geometrically, while the tail probability of queue 1 decays much faster than queue 2's. This helps us design an algorithm that computed the stationary distribution. Finally, by using the algorithm, we perform a sensitivity analysis on various system parameters, i.e., the arrival rates, service rates and the upgrade rate. The numerical study provides helpful insights into designing such service systems. [ABSTRACT FROM AUTHOR]