FIFO anomaly is unbounded

Virtual memory of computers is usually implemented by demand paging. For some page replacement algorithms the number of page faults may increase as the number of page frames increases. Belady, Nelson and Shedler constructed reference strings for which page replacement algorithm FIFO produces near twice more page faults in a larger memory than in a smaller one. They formulated the conjecture that 2 is a general bound. We prove that this ratio can be arbitrarily large

zCap: a zero configuration adaptive paging and mobility management mechanism

Today, cellular networks rely on fixed collections of cells (tracking areas) for user equipment localisation. Locating users within these areas involves broadcast search (paging), which consumes radio bandwidth but reduces the user equipment signalling required for mobility management. Tracking areas are today manually configured, hard to adapt to local mobility and influence the load on several key resources in the network. We propose a decentralised and self-adaptive approach to mobility management based on a probabilistic model of local mobility. By estimating the parameters of this model from observations of user mobility collected online, we obtain a dynamic model from which we construct local neighbourhoods of cells where we are most likely to locate user equipment. We propose to replace the static tracking areas of current systems with neighbourhoods local to each cell. The model is also used to derive a multi-phase paging scheme, where the division of neighbourhood cells into consecutive phases balances response times and paging cost. The complete mechanism requires no manual tracking area configuration and performs localisation efficiently in terms of signalling and response times. Detailed simulations show that significant potential gains in localisation effi- ciency are possible while eliminating manual configuration of mobility management parameters. Variants of the proposal can be implemented within current (LTE) standards

Truly Online Paging with Locality of Reference

The competitive analysis fails to model locality of reference in the online paging problem. To deal with it, Borodin et. al. introduced the access graph model, which attempts to capture the locality of reference. However, the access graph model has a number of troubling aspects. The access graph has to be known in advance to the paging algorithm and the memory required to represent the access graph itself may be very large. In this paper we present truly online strongly competitive paging algorithms in the access graph model that do not have any prior information on the access sequence. We present both deterministic and randomized algorithms. The algorithms need only O(k log n) bits of memory, where k is the number of page slots available and n is the size of the virtual address space. I.e., asymptotically no more memory than needed to store the virtual address translation table. We also observe that our algorithms adapt themselves to temporal changes in the locality of reference. We model temporal changes in the locality of reference by extending the access graph model to the so called extended access graph model, in which many vertices of the graph can correspond to the same virtual page. We define a measure for the rate of change in the locality of reference in G denoted by Delta(G). We then show our algorithms remain strongly competitive as long as Delta(G) >= (1+ epsilon)k, and no truly online algorithm can be strongly competitive on a class of extended access graphs that includes all graphs G with Delta(G) >= k- o(k).Comment: 37 pages. Preliminary version appeared in FOCS '9

Paging and Registration in Cellular Networks: Jointly Optimal Policies and an Iterative Algorithm

This paper explores optimization of paging and registration policies in cellular networks. Motion is modeled as a discrete-time Markov process, and minimization of the discounted, infinite-horizon average cost is addressed. The structure of jointly optimal paging and registration policies is investigated through the use of dynamic programming for partially observed Markov processes. It is shown that there exist policies with a certain simple form that are jointly optimal, though the dynamic programming approach does not directly provide an efficient method to find the policies. An iterative algorithm for policies with the simple form is proposed and investigated. The algorithm alternates between paging policy optimization and registration policy optimization. It finds a pair of individually optimal policies, but an example is given showing that the policies need not be jointly optimal. Majorization theory and Riesz's rearrangement inequality are used to show that jointly optimal paging and registration policies are given for symmetric or Gaussian random walk models by the nearest-location-first paging policy and distance threshold registration policies.Comment: 13 pages, submitted to IEEE Trans. Information Theor

On-Line File Caching

In the on-line file-caching problem problem, the input is a sequence of requests for files, given on-line (one at a time). Each file has a non-negative size and a non-negative retrieval cost. The problem is to decide which files to keep in a fixed-size cache so as to minimize the sum of the retrieval costs for files that are not in the cache when requested. The problem arises in web caching by browsers and by proxies. This paper describes a natural generalization of LRU called Landlord and gives an analysis showing that it has an optimal performance guarantee (among deterministic on-line algorithms). The paper also gives an analysis of the algorithm in a so-called ``loosely'' competitive model, showing that on a ``typical'' cache size, either the performance guarantee is O(1) or the total retrieval cost is insignificant.Comment: ACM-SIAM Symposium on Discrete Algorithms (1998