Minimizing the average cost of paging under delay constraints

Efficient paging procedures help minimize the amount of bandwidth expended in locating a mobile unit. Given a probability distribution on user location, it is shown that the optimal paging strategy which minimizes the expected number of locations polledE[L] is to query each location sequentially in order of decreasing probability. However, since sequential search over many locations may impose unacceptable polling delay,D, optimal paging subject to delay constraints is considered. It is shown that substantial reductions inE[L] can be had even after moderate constraints are imposed on acceptableD (i.e.,D<-3).Since all methods of mobility management eventually reduce to considering a time-varying probability distribution on user location, this work should be applicable to a wide range of problems in the area. most notably those with additive cost structures.     

Ensemble polling strategies for increased paging capacity in mobile communication networks

The process of finding a unit in a mobile communications system is called paging and requires the use of limited network resources. Although it is understood how to minimize the use of network resources and satisfy delay constraints when paging a single unit, optimal policies for paging multiple units are difficult to derive. Here we adapt single unit polling methods to obtain simple ensemble polling schemes for use with multiple units which can greatly increase the rate at which page requests can be processed while maintaining acceptable average delay. This revised version was published online in July 2006 with corrections to the Cover Date.     

Optimal Sequential Paging in Cellular Wireless Networks

In a high-capacity cellular network with limited spectral resources, it is desirable to minimize the radio bandwidth costs associated with paging when locating mobile users. Sequential paging, in which cells in the coverage area are partitioned into groups and paged in a non-increasing order of user location probabilities, permits a reduction in the average radio costs of paging at the expense of greater delay in locating the users. We present a polynomial time algorithm for minimizing paging cost under the average delay constraint, a problem that has previously been considered intractable. We show the conditions under which cluster paging, a simple heuristic technique proposed for use with dynamic location update schemes, is optimal. We also present analytical results on the average delay and paging cost obtained with sequential paging, including tight bounds.     

Optimal aggregation factor and clustering under delay constraints in aggregate sequential group paging schemes

This paper considers several optimization problems of sequential paging with aggregation mechanism which has been shown to reduce significantly the paging cost of a wireless communication system. An important problem is to find the optimal aggregation factor subject to a constraint on the average paging delay. Another problem is, given a cost function that depends on both paging cost and paging delay, how to find the optimal aggregation factor to minimize that cost function. We have formulated and shown that these can be solved nicely due to the monotonicity and convexity of the average paging cost function and paging delay function. We demonstrate that the optimization problems of the aggregate factor and subnet clustering are not separable. This leads to joint optimization problems of aggregation factor and clustering that are investigated in this paper. The paper presents different algorithms to solve these joint optimization problems using the monotonicity in the aggregation factor and the number of clusters of the average paging cost and delay with the unconstrained optimal clustering and the structures of the constrained optimal clustering.     

A crossing-tier location update/paging scheme in hierarchical cellular networks

Location update/paging strategies have been widely studied in the traditional single-tier cellular networks. We propose and evaluate a novel crossing-tier location update/paging scheme that can be used in a hierarchical macrocell/microcell cellular network. Location update is proceeded only in the macrocell tier, where a location area (LA) is made up by larger macrocells. A mobile user will stay in such a LA for longer time. Therefore, the cost on location update can be reduced due to the decreased frequency of location update. To reduce the paging delay, the paged mobile user will be searched in the macrocell tier only when the paging load is not high. Otherwise, it will be searched in the microcell tier, where a sequential searching method is applied. The operation for the scheme is simple, as the macrocell/microcell cellular network has the advantage because a mobile user can receive a signal from both a microcell and the overlaid macrocell. Analytical models have been built for cost and delay evaluation. Numerical results show that, at relatively low cost, the crossing-tier scheme also achieves low paging delay.     

A parallel shuffled paging strategy under delay bounds in wireless systems

In sequential paging schemes, the paging process is considered on per user basis. When an incoming call arrives to a mobile terminal (MT), the associated location area is divided into several paging areas (PAs) and PAs are paged one by one until the MT is found. Even though sequential paging algorithms can reduce the paging cost compared to the blanket-paging scheme, they introduce extra and unnecessary delay due to the fact that, during each paging cycle, unpaged cells are idle and unused in terms of paging. In this letter, a simple parallel shuffled paging strategy is proposed to reduce delay and improve performance. In the proposed scheme, multiple MTs can be paged in difference PAs in parallel. Our study shows that the proposed scheme outperforms both the sequential paging and the blanket paging in terms of discovery rate and queueing delay.     

State-based paging/registration: a greedy technique

For a mobile unit moving according to some ergodic stochastic process, we show how to minimize the expected average cost of paging and registration based on system state information. Specifically, we assume that both the system and mobile unit (user) have access to or can derive the following: the user location probability distribution as a function of time given the last location known to the system, and the time elapsed since this last known location. We then derive methods by which the user decides whether to register based on the following: current location (x), the time elapsed since last contact with the system (t), the paging cost F(x_t,x₀,t) to be incurred by the system at time t given the current location x_t and the last known location x₀, i.e., the user knows the paging strategy to be used by the system for each time t. If x and t define the system state, the method can be called “state based”. Since the optimization is based only on the current expected cost rate and not that of all registration intervals, the method is “greedy”. The greedy method was compared to a timer-based method using a simple diffusive motion process. Reductions in the average paging registration cost of approximately 10% were observed. The more striking improvement was a reduction in the variability of paging/registration costs by a factor of three. Thus, taking both cost and variability reduction as a performance measure, even suboptimal inclusion of location information in the registration decision affords substantial improvement     

Non-Blocking Pipeline Paging with Known Location Probabilities for Wireless Systems

Paging schemes for wireless systems have been well studied in the literature. However, most schemes are considered on per user basis. In these schemes, when an incoming call arrives at a mobile terminal (MT), a paging request (PR) is put in a queue. PRs are served in an FIFO manner. When a PR is served, a search process is carried out to find the corresponding MT in a location area (LA). Most schemes study how to achieve a better performance in terms of cost with/without delay constraints per PR, and totally ignore other PRs in the queue until the MT is found or all the cells in the LA have been paged. In this paper, we propose a non-blocking pipeline probability paging scheme, which assumes known knowledge on location probabilities of individual MTs, under a paging delay constraint, where the location probability of an MT in a cell is the probability that the MT is in the cell. The proposed scheme is independent of the number of PRs in the queue and the arrival rate of PRs. Our study shows that the proposed scheme outperforms both the sequential probability paging scheme with known knowledge on location probabilities of individual MTs and the blanket paging scheme in terms of discovery rate and the total delay. Finally, we study several optimization problems with quality of service constraint for the pipeline probability paging scheme.     

A novel sectional paging strategy for location tracking in cellular networks

In this letter, we propose a new paging technique, sectional paging, that reduces the paging cost while complying with the delay constraint for mobiles roaming with traceable patterns. Without having to install much additional complexity, the developed scheme predicts the likelihood of residence and assigns optimal paging boundaries. Thus while complying with the required delay constraints, quality-of-service (QoS) measures will not need to be sacrificed as a result of increasing the update threshold. Under the same network conditions and mobile characteristics, simulation results reveal that the usage of sectional paging is most suitable when the roaming pattern is either traceable or can be predicted with reasonable precision.     

Performance evaluation of pipeline paging under paging delay constraint for wireless systems

In this paper, we present a simple pipeline paging (PP) scheme, in which multiple paging requests (PRs) can be served in a pipeline manner in different paging areas. We analytically model the blanket paging (BP) scheme, the sequential paging (SP) scheme, and the PIP scheme so that discovery rate, total delay, paging delay, and cost are derived analytically as functions of traffic load. Extensive simulations are carried out to verity our analytical results. Our study shows that the PIP scheme outperforms both the BIP and SIP schemes in terms of discover rate while maintaining the same cost as the SIP scheme. The PIP scheme outperforms the SP scheme in terms of total delay and has a lower total delay than the BIP scheme when traffic load is high. We also show that, when the paging delay constraint D is large enough, the PIP scheme achieves almost 200 percent of discovery rate and 50 percent of cost of the BP scheme, whereas discovery rate of the SIP scheme is far less than that of the BP scheme. Furthermore, we solve the following two-optimization problems for the PIP scheme: 1) the minimization of discovery rate with a bound on total delay and 2) the minimization of cost with a bound on total delay. In case the cost factor is not considered but total delay is important, we propose an adaptive scheme: When the traffic is lower than a threshold, the BIP scheme is adopted; otherwise, the PIP scheme is used. In this case, the threshold value is explicitly derived.     

Design of location areas with QoS considerations in a cellular network

In this paper, we present a location area (LA) planning model which explicitly has more QoS-conscious constraints than any other models. In order to specify an acceptable level of QoS, paging delay time (PDT) and paging blocking rate (PBR) are introduced. The paging process is described by the M/M/c/K queuing system and queuing analysis is carried out to obtain PDT and PBR. Also, in the proposed model, the time-varying call arrival rates are used to define the paging load on each cell, which helps to reflect the pattern of incoming calls more precisely and subsequently to improve the QoS level. To evaluate the proposed model, some examples are solved along with the average rate model and the peak rate model. The results show that the proposed model has the capability to maintain the acceptable level of QoS with the reasonable location management cost, compared to other models. Also, the sensitivity analysis is performed to see the effect of PDT and PBR in the formulation and it turns out that both PBR and PDT are important elements of the QoS measure and influential to the location management cost.     

An adaptive location management scheme for mobile broadband cellular systems

This paper presents an adaptive location management strategy that considers both location updating and paging by evaluating realistic mobility patterns. It proposes the design of an adaptive macro-location area based on multi-registration adapted to the terminals’ trajectory to reduce location updates. The solution includes an estimation of residence probabilities in the areas of the multi-registered list. This facilitates the design of a sequential paging scheme that reduces the average paging cost. Results show the capability of the solution to adapt to mobility patterns and traffic conditions in the network to minimize the overall location cost. Furthermore, the multi-registration approach and the reduced complexity in both network infrastructure and mobile terminals make the solution suitable for new packet-based broadband cellular systems.     

A direction-based location update scheme with a line-pagingstrategy for PCS networks

On the problem of location update and terminal paging, many schemes using ring-paging strategies have been proposed. However, sequentially paging the rings surrounding the mobile user's last updated location may cause large paging cost. We propose a direction-based location update (DBLU) scheme using a line-paging strategy to reduce the paging cost. A moving direction identification mechanism using only simple computations detects the change of moving direction and updates the mobile's location. The numerical results show that our DBLU scheme achieves good performance when the paging cost is high     

Mobile user location update and paging under delay constraints

Wireless personal communication networks (PCNs) consist of a fixed wireline network and a large number of mobile terminals. These terminals are free to travel within the PCN coverage area without service interruption. Each terminal periodically reports its location to the network by a process calledlocation update. When a call for a specific terminal arrives, the network will determine the exact location of the destination terminal by a process calledterminal paging. This paper introduces a mobile user location management mechanism that incorporates a distance based location update scheme and a selective paging mechanism that satisfies predefined delay requirements. An analytical model is developed which captures the mobility and call arrival pattern of a terminal. Given the respective costs for location update and terminal paging, the average total location update and terminal paging cost is determined. An iterative algorithm is then used to determine the optimal location update threshold distance that results in the minimum cost. Analytical results are also obtained to demonstrate the relative cost incurred by the proposed mechanism under various delay requirements.     

Optimal decision strategies for paging in mobile cellular networks

A high‐level technical survey of paging in mobile cellular communication networks is presented in this paper. We view paging as an optimal decision problem and explore different strategies based on sequential decisions. The examined schemes concentrate on different perspectives of the problem, depending on the type of decisions and the amount of information available or exploitable by the system. This approach provides a useful categorization and an easy conceptual basis for their theoretical investigation, necessary for the deployment of advanced paging algorithms. Because of its suggested generality, the discussed framework is also laid as reference for further research. As modern networks evolve, more emphasis will be given towards optimization in all aspects of a network system. The schemes presented greatly reduce paging costs and can be used in cooperation with known location update strategies to make part of a real network location management system. Copyright © 2006 John Wiley & Sons, Ltd.     

移动IP网络中基于遗传算法的多步寻呼策略及性能分析

在移动IP网络中,层次移动IP协议可降低移动IP位置管理的信令消耗。该文研究支持寻呼的HMIPv6,提出了时延限制下的多步寻呼策略以及基于遗传算法的多步寻呼方案——根据移动节点的位置概率分布,采用遗传算法对寻呼区域内的所有子网进行分组,每步寻呼一个组,使平均寻呼信令开销达到或接近最优。此外,对HMIPv6、单步寻呼的HMIPv6以及基于遗传算法的多步HMIPv6寻呼方案的信令开销进行了比较分析,得出寻呼节省信令开销的必要条件。最后,给出一组数值结果以说明所提出的寻呼策略的有效性。     

An optimal paging scheme for minimizing signaling costs under delaybounds

This letter introduces a method for minimizing paging costs in wireless systems with delay constraints. An optimal partition algorithm is proposed and the corresponding paging procedure is provided. Numerical results demonstrate that the new scheme outperforms other previous schemes for uniform and nonuniform location probability distributions     

Dynamic multi-step paging scheme in PMIPv6-based wireless networks

In Proxy Mobile IP (PMIPv6) networks, proxy-registrations are performed even for idle MNs, resulting in unnecessary signaling traffic. Although there have been many IP paging techniques aimed at reducing the unnecessary location update, they focus only on Mobile IP (MIP) since they had been developed before PMIPv6 was proposed. Thus, adopting existing IP paging support is not sufficient to support mobility in PMIPv6 networks. For more efficient support, we propose a dynamic multi-step paging scheme that pages an MN in multiple incremental steps instead of flooding paging messages to a whole paging area to significantly reduce the signaling traffic caused by the proxy location updates in the PMIPv6 networks. In addition, to improve the paging delay performance that may be deteriorated by the multi-step paging, the proposed scheme configures paging area dynamically to raise the efficiency of locating MNs. The size of a paging area is designed to be determined based on the speed of an MN. We also develop a thorough analytical model for evaluating the performance of the proposed scheme compared with a static paging scheme in terms of the signaling cost and the paging delay. Thorough analysis and simulation demonstrate that in the PMIPv6 network, our paging scheme can significantly reduce the signaling cost for IP paging, achieving a shorter paging delay, compared to that of a paging scheme with a fixed paging area.     

Information-Theory Based Optimal Location Management Schemes for Integrated Multi-System Wireless Networks

In a multisystem environment where a mobile node can utilize multiple interfaces and simultaneously connect to multiple providers, new opportunities exist for efficient location management strategies spanning heterogeneous cellular wireless networks. In this paper, an integrated framework is developed for location management in such a multi-system, fourth generation (4 G) wireless networks. This information-theoretic framework allows each individual sub-system to operate fairly independently, and does not require the knowledge of individual sub-network topologies. An efficient location management in such a loosely coupled network is designed by having a mobile node view its movement as a vector-valued sequence, and then transmit this sequence in an entropy coded form to the network. We demonstrate how an intelligent, integrated paging strategy must consider the joint residence probability distribution of a mobile node in multiple sub-networks. We prove that the determination of an optimal paging sequence is NP-complete, and also propose an efficient greedy heuristic to compute the paging sequence, both without and with bounds on the paging delay. Three different location tracking strategies are proposed and evaluated; they differ in their degrees of centralized control and provide tradeoff between the location update and paging costs. Simulation experiments demonstrate that our proposed schemes can result in more than 50% savings in both update and paging costs, in comparison with the basic movement-based, multi-system location management strategy.     

A Combination of Optimal Partitioning and Location Prediction to Assist Paging in Mobile Cellular Networks

The correlated both in space and time user mobility behavior can aid significantly in the localization of a moving terminal in the network coverage area. However, there is always some uncertainty in mobile user position and a network-wide search cannot be done. Therefore, a predictive paging scheme must always be combined with a location update strategy and a compatible algorithm to conduct the search. In this paper, we introduce a new strategy that combines an optimal partitioning of the location area (LA) with a model to predict user movements, based on the additional information of the cell where the last interaction between the network and the terminal took place. We study the performance of the strategy under delay bounds and different mobility and call arrival characteristics. It is found that the new scheme further minimizes signaling costs and enhances previous sequential paging algorithms.