Narrow Results

We consider a multi-server queueing model in which arrivals occur according to a Markovian arrival process (MAP). There is a single-server and additional (backup) servers are added or removed depending on sets of thresholds. The service times are assumed to be exponential and the servers are assumed to be homogeneous. A comparison of this model to the classical MAP/M/c queueing model through an optimization problem yields some interesting results that are useful in practical applications. For example, we notice that positively correlated arrival process appears to benefit with the threshold type queueing model. We also give the minimum delay costs and the associated maximum setup costs so that the threshold type queueing model is to be preferred over the classical MAP/M/c model.

We study a MAP/M/c queueing system in which a group of servers take a simultaneous phase type vacation. The queueing model is studied as a QBD process. The steady-state analysis of the model including the waiting time distribution is presented. Interesting numerical results are discussed.

We consider a single server retrial queueing system in which arrivals occur according to a Markovian arrival process. An arriving customer finding an idle server will get service immediately; otherwise the customer enters into a retrial orbit. The system is subject to catastrophic failures at which time all customers in the system (the one in service as well as the customers, if any, in the orbit) are lost. The system undergoes a repair and after completion of a repair the server in the system will be available for service. The customers in the orbit try to reach the server by sending a signal at random times and get service if the server is idle at those times. While customers are waiting in the orbit, they may become impatient and leave the system after a random amount of time. Any arrival finding the server unavailable (due to busy or under repair) and cannot enter the orbit due to the buffer being full (in the case of finite buffer only) is considered lost. Under exponential assumption for all except for the arrivals, the queueing model (for both finite and infinite orbit sizes) is studied using matrix-analytic methods and the qualitative nature of the model is brought out through some illustrative numerical examples.

The common queueing problem has always focused on domestic and industrialized activities. Various improved models of queueing theory are widely used to solve problems. The aim of this paper is to deduce the exact solution of Bogoyavlenskii equation via direct extended modified algebraic method. In addition, we apply it to determine the upper and lower bounds through the semidefinite optimization packages software (SeDuMi). The suggested model indicated strong bounds in reasonable times, we obtain a definite value of $u_0=11.876$ of the function $u(x)$ over $[0,1]$ where $N=20$ in a time duration less than 60 s and a maximum value of $u_0=24.987$ where $N=50$ in a time frame of approximately 7 min. This study enriches the theoretical optimization queueing network and provides an analysis and decision making method for perfecting the theory.

Giving customers queue length information about a service system has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they provide will affect the performance of the system. To this end, we construct and analyze a two-dimensional deterministic fluid model that incorporates customer choice behavior based on delayed queue length information. Reports in the existing literature always assume that all queues have identical parameters and the underlying dynamical system is symmetric. However, in this paper, we relax this symmetry assumption by allowing the arrival rates, service rates, and the choice model parameters to be different for each queue. Our methodology exploits the method of multiple scales and asymptotic analysis to understand how to break the symmetry. We find that the asymmetry can have a large impact on the underlying dynamics of the queueing system.

In this paper, we study queueing systems with delayed information that use a generalization of the multinomial logit choice model as its arrival process. Previous literature assumes that the functional form of the multinomial logit model is exponential. However, in this work we generalize this to different functional forms. In particular, we compute the critical delay and analyze how it depends on the choice of the functional form. We highlight how the functional form of the model can be interpreted as an exponential model where the exponential rate parameter is uncertain. Furthermore, the rate parameter distribution is given by the inverse Laplace–Stieltjes transform of the functional form when it exists. We perform numerous numerical experiments to confirm our theoretical insights.

The Multi Priority Dual Queue (MPDQ) is a new scheduling regime shown to reduce congestion for multi-class traffic over conventional scheduling disciplines in isolation. As the MPDQ improves traffic congestion, most notably in communication systems, it is not necessary to include it at every node, or service centre, within a network. To gain insight into the advantages of a mixed MPDQ / First In First Out network with prioritised traffic, simulations are performed with and without a dual queue and various Quality of Service (QoS) criteria are obtained. Queueing networks containing differentiated traffic, also known as multi-class networks, are complicated to solve analytically using existing queueing theory techniques. We discuss the complications of exact solutions and describe how we used simulation to obtain performance statistics. We also look at high-class traffic under different offered loads, and provide a comparison of the delay characteristics. These findings provide communication service providers valuable information in determining the improvement in QoS to differentiated networks with the MPDQ. They also highlight the importance of simulation as a tool of evaluation of networks, and the best MPDQ network scenario.

In this paper, we introduce a bipartite matching model for matching markets with dynamic arrivals and departures. Different from classical models with a finite-time horizon, our model has a long-time horizon with infinite vertices. In our model, the matching goal is to maximize the ratio of matched vertices, i.e., matched ratio. We define two types of online algorithms, i.e., Greedy and Patient, analyze their performance with evaluation metrics of both upper bounds and competitive ratios, and conduct extensive simulations to validate our analysis. To further simulate the real situation, we extend our model with the user’s strategic behavior and prove the existence of a specific Nash equilibrium under a differentiated matching mechanism.