An all geometric discrete-time multiserver queueing system

In this work we look at a discrete-time multiserver queueing system where the number of available servers is distributed according to one of two geometrics. The arrival process is assumed to be general independent, the service times deterministically equal to one slot and the buffer capacity infinite. The queueing system resides in one of two states and the number of available servers follows a geometric distribution with parameter determined by the system state. At the end of a slot there is a fixed probability that the system evolves from one state to the other, with this probability depending on the current system state only, resulting in geometrically distributed sojourn times. We obtain the probability generating function (pgf) of the system content of an arbitrary slot in steady-state, as well as the pgf of the system content at the beginning of an arbitrary slot with a given state. Furthermore we obtain an approximation of the distribution of the delay a customer experiences in the proposed queueing system. This approximation is validated by simulation and the results are illustrated with a numerical example

A Variable Neighborhood Search Algorithm for the Vehicle Routing Problem with Simultaneous Pickup and Delivery

The demand of distribution and reverse logistics is drastically increasing. In order to absorb customers and improve customer satisfaction degree, the logistical services for returned goods are increasingly important. The vehicle routing problem with simultaneous pick-ups and deliveries (VRPSPD) is one of the major operations problems in reverse logistics research. This paper proposed a variable neighborhood search (VNS) algorithm to solve the combinatorial optimization problem. A Genetic Algorithm for VRPSPD is also developed and used as a reference for performance comparison. The algorithm can also solve the vehicle routing problem with backhaul and mixed load (VRPBM). An extensive numerical experiment is performed on benchmark problem instances available in literature. It is found that VNS gives good results compared to the existing algorithms

A queueing framework for routing problems with time-dependent travel times

Special Issue 'Quantitative aspects of transportation and logistics'status: publishe

Buffer and server allocation in general multi-server queueing networks

This paper deals with the joint optimization of the number of buffers and servers, an important issue since buffers and servers represent a significant amount of investment for many companies. The joint buffer and server optimization problem (BCAP) is a non-linear optimization problem with integer decision variables. The performance of the BCAP is evaluated by a combination of a two-moment approximation (developed for the performance analysis of finite generalservice queues) and the generalized expansion method (a well-known method for performance analysis of acyclic networks of finite queues). A standard non-linear optimization package is used to optimize the BCAP for a large number of experiments. A comprehensive set of numerical results is presented. The results show that the methodology is capable of handling the trade-off between the number of servers and buffers, yielding better throughputs than previously published studies. Also, the importance of the squared coefficient of variation of the service time is stressed, since it strongly influences the approximate optimal allocation

Upper Bounds on Performance Measures of Heterogeneous // Queues

In many real-life queueing systems, the servers are often heterogeneous, namely they work at different rates. This paper provides a simple method to compute tight upper bounds on two important performance measures of single-class heterogeneous multi-server Markovian queueing systems, namely the average number in queue and the average waiting time in queue. This method is based on an expansion of the state space that is followed by an approximate reduction of the state space, only considering the most probable states. In most cases tested, we were able to approximate the actual behavior of the system with smaller errors than those obtained from traditional homogeneous multiserver Markovian queues, as shown by GPSS simulations. In addition, we have correlated the quality of the approximation with the degree of heterogeneity of the system, which was evaluated using its Gini index. Finally, we have shown that the bounds are robust and still useful, even considering quite different allocation strategies. A large number of simulation results show the accuracy of the proposed method that is better than that of classical homogeneous multiserver Markovian formulae in many situations

Performance analysis of multi-server tandem queues with finite buffers and blocking

In this paper we study multi-server tandem queues with finite buffers and blocking after service. The service times are generally distributed. We develop an efficient approximation method to determine performance characteristics such as the throughput and mean sojourn times. The method is based on decomposition into two-station subsystems, the parameters of which are determined by iteration. For the analysis of the subsystems we developed a spectral expansion method. Comparison with simulation shows that the approximation method produces accurate results. So it is useful for the design and analysis of production lines