In large-scale wireless sensor networks (WSNs), when the consumption of hardware is limited, how to maximize the performance has become the research focus for improving transmission quality of service (QoS) of WSNs in recent years. This paper presents a new evaluation method for packet buffer capacity of nodes using queueing network model, whose packet buffer capacity is analyzed for each type node, when it is in the best working condition. In order to evaluate congestion situation in the queueing network, and to get real effective arrival rates and transmission rates in the model, holding nodes were added in the queueing network model, and equivalent queueing network model is expanded. We establish an M/M/1/N type queueing network model with holding nodes for WSNs and design approximate iterative algorithms. Experimental results show that the model is consistent with the real data. packet buffer capacity of nodes is an important factor in utilization of network nodes [13] . If a node of WSNs is blocked, and packet buffer set too small, the entire network data transmission and processing efficiency is not high. Therefore, when the consumption of hardware is limited, how to optimize the node packet buffer size and maximize the performance for WSNs has become a research focus for improving the Quality of Service (QoS) of WSNs transmission in recent years. In this paper, we consider that packet buffer capacity corresponds to the length of the waiting queue in the established limited capacity of the queueing network model. When the length of the waiting queue reaches the maximum, the node is blocked in the queueing network model. Therefore, a typical WSN is modeled by M/M/1/N type queueing network model. The method of modeling based on topology of nodes in WSNs and performance analysis of the packets buffer capacity have been proposed. According to the topology of WSNs and operational characteristics, arrival, transferring and leaving relationships of transmission nodes, boundary nodes and sink node are analyzed, and data flow balance equations are obtained. In order to evaluate the congestion situation in the queueing network, and get real effective arrival rates and transmission rates in the model, holding nodes were added in the queueing network model and equivalent queueing network model is expanded. By analyzing the queueing model with blocking probability, to obtain the performance index of system when it is in steady state, approximate iterative algorithms are designed. The performance parameters of nodes model in the WSNs are calculated using limited iteration times. The optimal values for packets buffer sizes settings are obtained for transmission nodes, boundary nodes and sink nodes. The remainder of this paper is organized as follows. The related work and problem statement are introduced in Section 2 and Section 3. Section 4 describes the modeling of WSN and analysis. Section 4.1 describes the modeling method of using open queueing network model for WSNs; the balance equations of data flow are established. In Section 4.2, the equivalent queueing network model is obtained, that holding nodes are added in the may be blocking nodes. The model parameters of blocking probability of data packets, the arrival rate and node transfer rate, all are analyzed in Section 4.3 using the equivalent queueing model. Section 5 designs iterative approximation algorithms for total arrival rate of nodes and effective arrival rate and transfer rate of nodes with blocking probability. Section 6 gives the numerical calculation and analysis of experimental results. The performance parameters of WSN nodes are calculated using iterative algorithms given in Section 5. According to the relationship curves between utilization and buffer size, the packets size of the optimal buffer settings are obtained for transmission nodes, boundary nodes and sink node, respectively. The correctness of modeling and analysis method is verified by experimental data of the WSNs. Section 7 contains the conclusion and future work. When the hardware has been implemented, it is difficult to adjust the node's hardware resources in accordance with specific needs. Therefore, researchers have proposed the need for large-scale WSN nodes modeling method [14] . Through performance evaluation of pre-setting nodes, optimal parameters of allocation for the hardware nodes are obtained. The current modeling method based on Petri nets [15, 16, 17] is suitable for macromodeling, but it is not a specific modeling technique for large-scale WSNs. Queueing network is an effective system-level modeling method, which is widely used in the modeling and performance analysis of computing and communication systems [18, 19] . It has many advantages that include a highly abstract and rich theory for modeling. In recent years, researches have made some progress on analyzing and improving network performance in the application of finite capacity queueing networks. Bisnik et al. [20] modeled random access multi-hops wireless networks as open G/G/1 queueing networks and used diffusion approximation in order to evaluate closed form expressions for the average end-to-end delay. In [21, 22] , Kouvatsos and Awan described the priorities and blocking mechanisms with open-loop queueing network performance analysis, and queueing network parameters on the approximation and error estimates. Özdemira et al. [23] presented two Markov chain queueing models with M/G/1/K queues, which have been developed to obtain closed-form solutions for packets delay and packets throughput distributions in a real-time wireless communication environment using IEEE 802.11 DCF. Mann et al. [24] developed a queueing model for analyzing resource replication strategies in WSNs, which can be used to minimize either the total transmission rate of the network or to ensure that the proportion of query failures does not exceed a predetermined threshold. In [20] , Liehr et al. introduced enhancements to the standard of extended queuing network models, which allow the modeling and the simulation of inter-process communication and highlight the benefits granted by their enhanced EQN approach. However, these researches don't address the packet buffer capacity of nodes and how to set the buffer size to derive the optimal performance of the nodes in WSNs. Data packets are transmitted and processed in collaboration by the sink nodes, transmission nodes and boundary nodes. For a large scale WSN, a queueing network model can be used to analyze its performance [25, 26] . But how to configure resources to find the best value hardware using trends of changing the parameters of performance is an important reference for node design. The definition of the threshold of node buffer capacity is given below: Definition 1. When the queueing network system is stable, node's hardware buffer capacity just accommodate the maximum length of the queue
al REF presents a evaluation method for packet buffer capacity of nodes using queueing network model, whose packet buffer capacity analyzed for each type node.
A packet buffer evaluation method exploiting queueing theory for wireless sensor networks
Comput. Sci. Inf. Syst.
Comput. Sci. Inf. Syst.
Computer Science