Exact tail asymptotics for a three-dimensional Brownian-driven tandem queue with intermediate inputs

In this paper, we consider a three-dimensional Brownian-driven tandem queue with intermediate inputs, which corresponds to a three-dimensional semimartingale reflecting Brownian motion whose reflection matrix is triangular. For this three-node tandem queue, no closed form formula is known, not only for its stationary distribution but also for the corresponding transform. We are interested in exact tail asymptotics for stationary distributions. By generalizing the kernel method, and using extreme value theory and copula, we obtain exact tail asymptotics for the marginal stationary distribution of the buffer content in the third buffer and for the joint stationary distribution.

Towards the analysis of the performance measures of heterogeneous networks by means of two-phase queuing systems

Due to a multistage nature of transmission processes in heterogeneous 4G, 5G mobile networks, multiphase queuing systems become one of the most suitable ways for the resource allocation algorithms analysis and network investigation. In this paper, a few scientific papers that approached heterogeneous networks modelling by means of multiphase queuing systems are reviewed, mentioning the difficulties that arise with this type of analytical analysis. Moreover, several previously investigated models are introduced briefly as an example of two-phase systems of finite capacity and a special structure in discrete time that can be used for analysing resource allocation schemes based on the main performance measures obtained for wireless heterogeneous networks. One of the model presents a two-phase tandem queue with a group arrival flow of requests and a second phase of the complex structure that consists of parallel finite queues. The second model is a two-phase tandem queue with Markov modulated geometric arrival and service processes at the first phase and exhaustive service process at the second phase, which solves a cross-layer adaption problem in a heterogeneous network.

Importance sampling for Markovian tandem queues using subsolutions: exploring the possibilities

We consider importance sampling simulation for estimating the probability of reaching large total number of customers in an [Formula: see text] tandem queue, during a busy cycle of the system. Our main result is a procedure for obtaining a family of asymptotically efficient changes of measure based on subsolutions. We explicitly show these families for two-node tandem queues and we find that there exist more asymptotically efficient changes of measure based on subsolutions than currently available in literature.

Smart Policies for Multisource Inventory Systems and General Tandem Queues with Order Tracking and Expediting

We study an inventory system with multiple supply sources and expediting options. The replenishment lead times from each supply source are stochastic, representing congestion and disruption. We construct a family of smart ordering and expediting policies that utilize real-time supply information. Such dynamic policies are generally difficult to evaluate, because the corresponding supply system is a tandem queue with state-dependent arrivals and routing, whose queue-length steady-state distribution is usually not in product form. Our main result is to identify two appealing special cases of the general policy, Policy-M and Policy-E, which possess simple product-form solutions and lead to closed-form performance measures. Policy-M retains full sourcing flexibility, but ignores upstream congestion in making expediting decisions. Policy-E only orders from the normal, farthest source, but makes expediting decisions based on both upstream and downstream information. A numerical study shows that the best Policy-M leads to a lower average cost than the best Policy-E in almost all cases. Also, implementing the best Policy-M parameters, the general policy only performs slightly better than Policy-M. These observations reveal the value of combining sourcing flexibility with some, but limited, dynamic expediting. Our findings are equally applicable to the equivalent tandem queue. They thus may aid dynamic routing and expediting decisions for online retailers and logistics providers, among others.

Performance measures of parallel tandem open queueing network

Purpose The authors consider parallel four-state tandem open queueing network. The queue capacity is infinite. Passenger arrival rate is Poisson distribution and service rate is exponential distribution. The queue is constructed in the form of tandem queue, and each and every queue of tandem queue is single server (M/M/1) queue. In tandem queue, passengers will leave the system once they receive service from both the states. The purpose of this paper is to provide performance analysis for four-state tandem open queue network, and a governing equation is formulated with the help of transition diagram. Using Burke theorem, the authors formulated equation for average number of passenger in the system, average waiting time of passenger in the system, average number of passenger in the queue and average waiting time of passenger in the queue. Design/methodology/approach This paper used Burke’s theorem. Findings In this paper, performance analysis is done for parallel four-state tandem open queueing network and performance measure solved using Burkes theorem formula. K. Sreekanth et al. has done performance analysis for single tandem queue with three states. In this paper, the authors have done performance analysis for two tandem queues parallel with four states. This four-state tandem open queueing network is suitable for real world applications. This paper can extend for more number of service states and multi-server states according to the application, and in such case, the authors have to prove and explain with numerical examples. This analysis is more useful for the applications such as airports, railway stations, bus-stands and banks. Originality/value In this paper, parallel four-state tandem open queueing network and performance measure has been solved using Burke’s theorem formula.