A tandem queueing system with applications to pricing strategy

In this paper, we study the total workload process and waiting times in a queueing system with multiple types of customers and a first-come-first-served service discipline. An M/G/1 type Markov chain, which is closely related to the total workload in the queueing system, is constructed. A method is developed for computing the steady state distribution of that Markov chain. Using that steady state distribution, the distributions of total workload, batch waiting times, and waiting times of individual types of customers are obtained. Compared to the GI/M/1 and QBD approaches for waiting times and sojourn times in discrete time queues, the dimension of the matrix blocks involved in the M/G/1 approach can be significantly smaller.

We consider queueing systems in which the service rate is the controlled variable. The cost depends on the queue length and selected rate. The objective is to choose the service rate dynamically, based on the state of the system so as to minimize the average cost over an infinite horizon. Six classes, either known in the literature or new, are studied in detail: queueing systems with vacations, single-server queueing systems with and without switching costs, and tandem queueing systems with and without service costs. A novel approach is presented here using fuzzy control to solve these problems. Simulation shows that the approach is efficient and promising, especially in cases where analytical solutions do not exist.

A tandem retrial queueing system with two Markovian flows and reservation of channels

Given the importance of determining the traffic level in celebrity endorsement management and prominent impacts from strategic consumers, this paper utilizes mathematical modelling to study the optimal traffic level and pricing strategy as well as relevant influencing factors in the context of celebrity endorsement. The results show that optimal traffic level is highest under uniform high pricing strategy and lowest under uniform low pricing strategy, with that of dynamic pricing strategy lying in between. Aside from the proportion of strategic consumers, optimal pricing strategy is also determined by the joint effects of celebrity endorsement characteristics, such as the premium effect of celebrity endorsement, the market demand expansion effect, and the traffic using cost. It depends on the tradeoff between the positive effects (premium effect and market demand expansion effect) and the negative effects (endorsement fee of unit traffic) of the celebrity endorsement.

Optimal pricing and inventory strategies for fashion products under time-dependent interest rate and demand

We consider congestion control in a nonstationary queueing system. Assuming that the arrival and service rates are bounded, periodic functions of time, a Markov decision process (MDP) formulation is developed. We show under the infinite horizon discounted and average reward optimality criteria, for each fixed time, optimal pricing and admission control strategies are nondecreasing in the number of customers in the system. This extends stationary results to the nonstationary setting. Despite this result, the problem still seems intractable. We propose an easily implementable pointwise stationary approximation (PSA) to approximate the optimal policies, suggest a heuristic to improve the implementation of the PSA and verify its usefulness via a numerical study.

In this paper we develop an economic order quantity model to investigate the optimal replenishment policies for instantaneous deteriorating items under inflation and trade credit. Demand rate is a linear function of selling price and decreases negative exponentially with time over a finite planning horizon. Shortages are allowed and partially backlogged. Under these conditions, we model the retailer’s inventory system as a profit maximization problem to determine the optimal selling price, optimal order quantity and optimal replenishment time. An easy-to-use algorithm is developed to determine the optimal replenishment policies for the retailer. We also provide optimal present value of profit when shortages are completely backlogged as a special case. Numerical examples are presented to illustrate the algorithm provided to obtain optimal profit. And we also obtain managerial implications from numerical examples to substantiate our model. The results show that there is an improvement in total profit from complete backlogging rather than the items being partially backlogged.

Energy efficiency (EE) level has become an essential environmental index of products and can be improved by EE innovation. With consideration of EE level evolution and market differentiation, an optimal control model under a two-market framework is proposed to investigate EE innovation and two-stage pricing strategies. Impacts of consumer environmental awareness (CEA) and EE standard on optimal investment and pricing strategies are discussed. Results indicate that environmental awareness and standard result in strategy shift. As environmental awareness increases, the EE level driven by investment strategy may switch from staying in traditional market, to expanding markets by entering the green market and remaining at the standard, till capturing the green market and keeping above that standard. Impacts of standard on strategy shift exhibit a tricky trend. For loose and appropriate standards, the producer prefers to invest more to expand market by entering the green market with the increase of standard. However, a stringent standard may prevent the producer from entering the green market. In addition, optimal prices in both stages are positively impacted by the CEA and the standard.

Tandem queueing system with impatient customers as a model of call center with Interactive Voice Response

We introduce the concept of fresh data trading, in which a destination user requests, and pays for, fresh data updates from a source provider, and data freshness is captured by the age of information (AoI) metric. Keeping data fresh relies on costly frequent data updates by the source, which motivates the source to price fresh data. In this work, the destination incurs an age-related cost, modeled as a general increasing function of the AoI. The source designs a pricing mechanism to maximize its profit, while the destination chooses a data update schedule to trade off its payments to the source and its age-related cost. Depending on different real-time applications and scenarios, we study both a finite-horizon model and an infinite-horizon model with time discounting. The key challenge of designing the optimal pricing scheme lies in the destination's time-interdependent valuations, due to the nature of AoI, and the infinite-dimensional dynamic optimization. To this end, we exploit three different dimensions in designing pricing by studying three pricing schemes: a time-dependent pricing scheme, in which the price for each update depends on when it is requested; a quantity-based pricing scheme, in which the price of each update depends on how many updates have been previously requested; and a simple subscription-based pricing scheme, in which the price per update is constant but the source charges an additional subscription fee. Our analysis reveals that (1) the optimal subscription-based pricing maximizes the source's profit among all possible pricing schemes under both finite-horizon and infinite-horizon models; (2) the optimal quantity-based pricing scheme is only optimal with a finite horizon; and (3) the time-dependent pricing scheme, under the infinite-horizon model with significant time discounting, is asymptotically optimal. Numerical results show that the profit-maximizing pricing schemes can also lead to significant reductions in AoI and social costs, and that a moderate degree of time discounting is enough to achieve a close-to-optimal time-dependent pricing scheme.

In this paper, we study a service provider with opaque price strategy who sells services to loss-averse customers in a congestion-prone facility. The opaque price strategy means that the service provider discloses a price range of services to potential customers through social media. Loss aversion aims to characterize customers' reference-dependent preferences. We analyze a queueing game model with the help of an M/M/1 queueing system and adopt the cutoff structure characterized by reservation price to represent the loss-averse customers' joining decision. Then, we derive the loss-averse customer's reservation price and queueing strategies at equilibrium. In addition, the service provider sets the price to maximize her profit. We obtain some insights into how customers' degree of loss aversion affects the service provider's optimal price. For example, customers with a higher degree of loss aversion on the waiting time and the payment would push the service provider to decrease the optimal price. Customers with a higher degree of loss aversion about the service reward would urge the service provider to increase the optimal price. Furthermore, considering the attachment effect, we obtain the lowest possible expected profit of the service provider.

The assignment of extra servers to stations in Tandem Queueing systems with small or no buffers

Based on the sharing economy, crowdsourcing logistics services share social delivery freelancers instead of traditional full-time delivery employees. The optimal dynamic pricing model of crowdsourcing logistics services, which could be applied to adjust the social delivery capacity supply to meet the stochastic demand especially during the peak period, is established based on optimal control theory. We study optimal pricing strategies under both conditions when the supply and the demand is balanced and accumulated delivery orders are minimized. Moreover, the impact of delivery riders’ wage ratio on pricing and platforms’ expected revenue are analyzed. It is verified by numerical simulation results that optimal dynamic pricing strategies of crowdsourcing logistics services could effectively balance supply and demand, further maximize the expected revenue of platforms. The growth rate of optimal pricing of crowdsourcing logistics services is increasing with respect to the delivery riders’ wage ratio. However, the expected revenue of crowdsourcing logistics platforms declines as the wage ratio increases.

This study investigates the optimal pricing strategies of the server and the equilibrium behaviors of customer in the discrete-time Geo/Geo/1 queueing system. In this work, we consider two pricing models. The first one is called the ex-ante payment (EAP) scheme where the server charges a flat price for all services. The second one is called the expost payment (EPP) scheme where the server charges a price that is proportional to the time that a customer spends in the system. Based on the reward-cost structure, the server should make the optimal pricing decisions in order to maximize its expected profit per unit time in each payment scheme. This study also investigates customer’s equilibrium joining or balking behaviors under server’s optimal pricing strategies under the corresponding pricing models. Numerical experiments are conducted to help the server best select one between two pricing models. The work results could provide the managers with reference information on the pricing problem in the queueing system.

Cost-Per-Impression Pricing for Display Advertising