Miaomiao Yu

This study investigates price decisions in a queue with two servers, where customers exhibit retrial behavior. There is no waiting space. Arrival customers have the option to either join the system or balk; when the two servers are occupied, those who decide to enter become repeat customers. Two scenarios where the waiting lines in orbit are unobservable and observable are considered. We analyze customers’ behavior and derive their Nash equilibrium strategies under both cases. Additionally, we examine optimal pricing decisions aimed at maximizing profit and social welfare, respectively. Moreover, we demonstrate that these objectives often lead to divergent outcomes. Compared to a single-server queue, the reduction in customers’ sojourn time is more obvious when the waiting line is unobservable. Under certain conditions—such as a large potential market size, high customer impatience, or a low retrial rate—increasing the number of service personnel can enhance both profit and social welfare. Notably, a profit-maximizing manager is more incentivized to increase servers than the social planner. These findings provide valuable insights for balancing operational efficiency, profitability, and customer satisfaction in queue management systems.

We consider a shock and wear model in which the inter-shock arrival process is a phase-type (PH) renewal process, and the system’s lifetime is generally distributed. The system has two competing failure modes. One failure mode is due to random shocks, which cause failure by overloading the system. The other failure mode is owning to wear-out failures, which usually happen after the system has run for many cycles. System failure is not self-announcing and remains undiscovered unless an inspection is performed. The intervals between successive inspections are identical and equal to T time units. If a system failure is detected, the corrective repair or replacement is conducted immediately. If the system is found working at inspection, preventive maintenance will be carried out to prolong its useful life. Furthermore, to model the occurrence of events with an underlying monotonic trend, the extended geometric process (EGP) is employed to account for the impact of different types of failures on the system’s degradation. Moreover, for establishing the cost rate function in our model, the counting process generated from a PH renewal shock process is studied in detail using the roots method and formula for calculating residues. Based on these results, the survival function and other characteristics of the system are further investigated. Finally, numerical examples that determine the optimal inspection period T[ ] and the optimal replacement policy N[ ], which minimizes the long-run average cost rate, are presented.

As the queue becomes exhausted, different maintenance tasks can be performed according to the fatigue load and wear degree of the service equipment. At the same time, considering the customer's sensitivity to time delay, the service facility will not completely remain inactive during the maintenance period. To describe this objectively existing phenomenon arising in the waiting line system, we consider a hyper-exponential working vacation queue with a batch renewal arrival process. Through the calculation of the well-structured roots of the associated characteristic equation, the shift operator method in the theory of difference equations and the supplementary variable technique for stochastic modeling plays a central role in the queue-length distribution analysis. Comparison with other ways to analyze queueing models, the advantage of our approach is that we can avoid deriving the complex transition probability matrix of the queue-length process embedded at input points. The feasibility of this approach is verified by extensive numerical examples.

To prevent overcrowding during the COVID-19 pandemic, numerous businesses, and public service systems have to limit the number of people entering the premises to reduce infection risks. Such a realistic situation prompts us to revisit an adaptive queueing model from a statistical perspective, which allows us to extensively analyze and explore the stochastic service system arising in the pandemic period. In order to avoid long waiting lines, we assume that the arrival rate of customers into the system depends on the system size instead of a constant rate. This article attempts to study the uniformly minimum variance unbiased estimators and closed-form Bayes estimators of various queueing characteristics, such as the probability that the server is busy, the proportion of lost customers, mean system length, and average queue length. The estimates and their behaviors are compared by Monte-Carlo simulation with different sample sizes. The simulation results show that we may choose different estimation techniques for different performance indicators to obtain a more precise estimate.

The purpose of this paper is to present an alternative algorithm for computing the stationary queue-length and system-length distributions of a single working vacation queue with renewal input batch arrival and exponential holding times. Here we assume that a group of customers arrives into the system, and they are served in batches not exceeding a specific number b. Because of batch arrival, the transition probability matrix of the corresponding embedded Markov chain for the working vacation queue has no skip-free-to-the-right property. Without considering whether the transition probability matrix has a special block structure, through the calculation of roots of the associated characteristic equation of the generating function of queue-length distribution immediately before batch arrival, we suggest a procedure to obtain the steady-state distributions of the number of customers in the queue at different epochs. Furthermore, we present the analytic results for the sojourn time of an arbitrary customer in a batch by utilizing the queue-length distribution at the pre-arrival epoch. Finally, various examples are provided to show the applicability of the numerical algorithm.

In this paper we consider a discrete-time Geo/G/1 queue with delayed Min(N, D)-policy. Using renewal process theory, total probability decomposition technique and z-transform, we study the transient and equilibrium properties of the queue length from an arbitrary initial state, and obtain both the recursive expressions of the transient state queue length distribution and the steady state queue length distribution at arbitrary time epoch n⁺. Furthermore, we derive the important relations between equilibrium queue length distributions at different time epochs n^–, n and n⁺. Finally, we give some numerical examples about capacity decision in queueing systems to demonstrate the application of the analytical results reported in this paper.

A new isoflavonolignan glycoside, namely cantoniensin A (1), along with three known compounds were isolated from Abrus cantoniensis. The structure of the new compound was elucidated on the basis of spectroscopic analyses, including 1D-, 2D-NMR and HRESIMS. Compound 1 is the second example of isoflavonolignan glycoside from nature and is also the first isoflavonolignan isolated from the genus of Abrus.