In this work, we consider a novel single-server retrial queue with event-dependent arrival rates. Contrary to other related works, the primary customers’ arrival rates depend on the last realized ...event, which refers either to a departure, or to an arrival of either type, or to when a customer arrives during a busy period, compared with others. Our motivation stems from the modeling of service systems, in which the customers express their willingness to join the system based on the last realized event. We investigate the stability conditions, and derive the stationary distribution both at service completion epochs, and at an arbitrary epoch. We also study the asymptotic behaviour under high rate of retrials. Performance measures are explicitly derived, and extensive numerical examples are performed to investigate the impact of event-dependency. Moreover, constrained optimisation problems are formulated and solved with ultimate goal to derive optimal joining probabilities.
Traffic management is a critical activity, the population is increasing day by day and so the traffic on the road is also increasing. Traffic jams and long waiting queues of vehicles at the road ...crossing are now part of everyone's life. The traffic lights used at the crossing to regulate the traffic play a vital role in the smooth functioning of traffic movement. At a crossing of four roads, it has been observed that giving an equal amount of green light to all roads is meaningless since the arrival of traffic on different paths is different. Importantly, the arrival rate is responsible for all traffic jams, long queues, and increased waiting time. Therefore, this paper suggests a green light allocation scheme for all paths i depending on the arrival rate of the vehicles. Thus, the allocation of green light will be dynamic. Further, weight is also computed, where more arrival rate means more weight, thereby assigning more time to the green signal. This will help in reducing the long queue length, residual traffic, and long waiting times. On simulating the traffic with the traffic data, the proposed optimized green light allocation scheme to path i reduces the residue traffic to negligible, allowing smooth traffic flow even during peak hours. The work also provides a proficient optimization of the waiting time of vehicles accumulated during the red light. According to the simulation, the maximum time assigned for the green signal during the peak hour of 9:30 AM to 10:00 AM for paths i, where 1≤i≤4 is 39.96, 33.36, 26.64, and 20.04 seconds respectively. Similarly, during the second rush hour of 5:00 PM to 6:00 PM, the simulation assigns a green signal time of 41.4, 37.2, 24.84, and 16.56 seconds for corresponding paths 1–4. Thus, the proposed work suggests an effective traffic management scheme at the four-road crossing.
•explores the arrival rate of rainfall drops at the ground.•demonstrates importance for understanding soil erosion processes.•presents drop arrival rate data presently difficult to obtain.•discusses ...potential implications for rainfall simulation experiments.
Rainfall drop arrival rate (DAR) quantifies the number of impacts at the ground of drops of varying size per unit area and time. It can be calculated from the drop size distribution and fall speed data used for rain integral parameters such as total kinetic energy or rainfall intensity. However, the DAR can also be calculated for individual drop size classes, revealing the relative number of impacts of small and large drops. New calculations of DAR are developed, and show that for increasingly intense rain, impacts by drops of large diameters become more common, and contribute an increasing proportion of the total kinetic energy. This may exert an important influence on many landsurface processes. A comparison with the kinds of rainfall arrival rates present in simulated rainfall is made, and suggests that although simulated rainfall may be generated with an intensity corresponding to natural rain, the DAR, especially for small and large drops, is often significantly different to the value expected in natural rain. For research on soil splash, interrill erosion, infiltration, and other important land surface processes, it is suggested that attention to DAR may prove informative, both as a potentially useful explanatory variable in field studies made under natural rainfall, and as a target parameter in the design of rainfall simulation experiments.
We review queueing‐theory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not ...straightforward, because standard queueing theory focuses on the long‐run steady‐state behavior of stationary models. We show how to adapt stationary queueing models for use in nonstationary environments so that time‐dependent performance is captured and staffing requirements can be set. Relatively little modification of straightforward stationary analysis applies in systems where service times are short and the targeted quality of service is high. When service times are moderate and the targeted quality of service is still high, time‐lag refinements can improve traditional stationary independent period‐by‐period and peak‐hour approximations. Time‐varying infinite‐server models help develop refinements, because closed‐form expressions exist for their time‐dependent behavior. More difficult cases with very long service times and other complicated features, such as end‐of‐day effects, can often be treated by a modified‐offered‐load approximation, which is based on an associated infinite‐server model. Numerical algorithms and deterministic fluid models are useful when the system is overloaded for an extensive period of time. Our discussion focuses on telephone call centers, but applications to police patrol, banking, and hospital emergency rooms are also mentioned.
Corridor with corner may be the potential bottleneck in subway station, and walking behavior of passengers around corner is random. In this study, walking process of passenger around corner is ...divided into five phases according to field survey, i.e., pre-turning straight-going, ready-turning, turning, distance-adjusting and post-turning straight-going. An advanced social force model is proposed to model the turning behavior of passenger around corner, taking visual angle, walking preference and steering force into consideration. To improve walking efficiency, the influences of geometry of facility, walking preference of passengers and arrival rate of passenger flow are investigated. Results show when angle of corner is less than 120°, the walking speed slows down sharply and walking time extends. To improve the walking efficiency, passengers can be guided to walk in lines orderly. The maximum of throughput can be obtained with proper arrival rate. Once the volume of passengers exceeds the facility capacity, effects of “stop-and-go” and “faster is slower” will occur around corner.
•Analyzing and demonstrating the walking process of passengers around corner.•Modeling movement of turning passengers with advanced social force model.•Verifying the proposed model with controlled experiments.•Quantifying arrival rate and corner angle influencing on walking efficiency.
Software-defined networking (SDN) is a cutting-edge technology, featuring a centralized control that facilitates, e.g., flexible deployment of unmanned aerial vehicles (UAVs). On the other hand, ...UAV-enabled communication is a promising technology due to its numerous traits such as the ability of on-demand deployment and the high likelihood of strong line-of-sight (LoS) communication links. However, UAV-enabled communication suffers non-perpetual nodes and intermittent communication links. Fortunately, SDN provisions an unparalleled global vision on such dynamic network architecture to overcome the challenges of loose links and disappearing nodes. On the other hand, there are catastrophic or remote regions where a UAV-mounted base station (BS) potentially functions without a terrestrial BS, albeit a WiFi access point (AP) may still exist. Therefore, this paper considers software-defined coexisting UAV-mounted BS (UBS) and WiFi AP, and investigates the queuing delay behavior via the UBS positioning and the AP traffic offloading. The subscribers (users) are divided into cellular subscribers (CSs) and WiFi subscribers (WSs). A CS is connected to the UBS and is possibly granted simultaneous access to the AP, leading to WiFi traffic offloading. Leveraging the software-defined global view, the objective of a software-defined controller (SDC) is to minimize the average M/M/1 queuing delay of the CSs, while guaranteeing the delay performance for the WSs, via optimizing the spectrum allocation, the UBS position, the CS association to the AP, and the CS traffic offloading. The optimization problem is non-convex, comprising binary variables, for which we use the block coordinate descent and successive convex approximation methods to find a high-quality solution. Numerical results verify that our solution achieves significant performance gains over benchmark schemes.
Accurate real-time state estimation plays an important role in distributed generation (DG) networks. In order to establish a reliable communication link for estimation, an information-centric ...networking (ICN) was employed with the development of smart grids technology. However, the widespread adoption of DG network boosts the amount of data transmitted through ICN, which is now the real-time performance bottleneck of estimation. By fully considering the nonlinearity of DG system, this paper develops an event-trigger particle filter (ET-PF) to relieve the communication burden and achieve an appropriate estimation accuracy. An arrival rate guaranteed event-trigger strategy is established for saving the bandwidth at first, which selects only the observations containing innovational information for the purpose of filtering. When the observation is not triggered, an ET-PF filtering algorithm is further proposed, making full use of the information from the prior event-trigger strategy, to enhance the performance of estimation. The design-oriented guaranteed arrival rate, specifically designed by ET-PF in statistical sense, is beneficial to design ICN infrastructure. Finally, its feasibility and performance is demonstrated using the standard IEEE 39-bus system with phasor measurement units.
We consider a general unobservable queueing model in which customers are allowed to join or balk upon arrival. The service provider charges the same admission fee to all joining customers. All ...joining customers receive the same reward and incur heterogeneous waiting cost rates. We show that the socially optimal arrival rate is greater than or equal to the profit maximizing arrival rate. Equivalently, the socially optimal admission fee is smaller than or equal to the profit maximizing admission fee.
In many service systems, the staffing decisions must be made before the arrival rate is known with certainty. Thus, it is more appropriate to consider the arrival rate as a random variable at the ...time of the staffing decision. Motivated by this observation, we study the staffing problem in a service system modeled as an Erlang-A queue facing a random arrival rate. For linear staffing costs, linear waiting costs, and a cost per customer abandonment, we propose a policy that is based on modifying the well-known square-root safety staffing policy to explicitly account for the randomness in the arrival rate. Our primary contribution is to show that our proposed policy is “universally optimal”, i.e., irrespective of the magnitude of randomness in the arrival rate, the optimality gap between our proposed policy and the exact optimal policy remains bounded as the system size grows large. This is important because earlier performance guarantees for Erlang-A queues either (1) are not universal and offer performance guarantees that depend on the magnitude of uncertainty in the arrival rate or (2) are universal but assume a deterministic arrival rate. The practical relevance of this provable robustness is that our proposed policy is a “one-size-fits-all” as it is guaranteed to perform well for all levels of arrival rate uncertainty.
In reality, vehicles and pedestrians are delayed for their interference with each other at the crosswalk, or by the unreasonable allocation of traffic light time. Especially under the popular rule of ...vehicles yield to pedestrians in front of the crosswalk, traffic flow are seriously affected. In this paper, the effects of pedestrian traffic light and the related parameters on traffic flow are studied. On the road, the Nagel–Schreckenberg (NaSch) model is conducted to simulate the scenario with and without pedestrian traffic light. Results show that, vehicle traffic flow can be effectively improved with pedestrian traffic light. Moreover, the optimization of pedestrian waiting time with different vehicle and pedestrian arrival rates are obtained from comprehensive simulations. Finally, effects of some other parameters are briefly discussed.
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