The Conference Call Search Problem in Wireless Networks

Abstract

Cellular telephony systems, where locations of mobile users are unknown at some times, are becoming more common. In such systems, mobile users are roaming in a zone and a user reports its location only if it leaves the zone entirely. The Conference Call Search problem (CCS) deals with tracking a set of mobile users in order to establish a call. To find a single roaming user, the system may need to search each cell where the user may be located. The goal is to identify the location of all users, within bounded time, satisfying some additional constraints on the search scheme. We consider cellular systems with n cells and m mobile users (cellular phones). The uncertain location of users is given by m probability distribution vectors. Whenever the system needs to find the users, it conducts a search operation lasting at most d rounds. A request for a single search step specifies a user and a cell. In this search step, the cell is asked whether the given user is located there. In each round the system may perform an arbitrary number of such requests. An integer number B ≥ 1 bounds the number of distinct requests per cell in every round. The bound d results from quality of service considerations whereas the bound B results from the wireless bandwidth allocated for signaling being scarce. Every search step consumes expensive wireless links, which motivates search techniques minimizing the expected number of requests thus reducing the total search costs. We distinguish between oblivious, semi-adaptive and adaptive search protocols. An oblivious search protocol decides on all requests in advance, and stops only when all users are found. A semi-adaptive search protocol decides on all the requests in advance, but it stops searching for a user once it is found. An adaptive search protocol stops searching for a user once it has been found (and its search strategy may depend on the subsets of users that were found in each previous round). We establish the difference between those three search models. We show that for oblivious "single query per cell" systems (B = 1), and a tight environment (d = m), it is NP-hard to compute an optimal solution (the case d = m = 2 was proven to be NP-hard already by Bar-Noy and Naor) and we develop a PTAS for these cases (for fixed values of d = m). However, we show that semi-adaptive systems allow polynomial time algorithms. This last result also shows that the case B = 1 and d = m = 2 is polynomially solvable also for adaptive search systems, answering an open question of Bar-Noy and Naor.

Adaptive paging schemes for group calls in mobile broadband cellular systems

“…We consider that paging is performed on a unique group identifier, known by the members of the group, so that a single paging message in a cell is enough to find all users belonging to that group. In this way, the number of users that can be simultaneously searched in a cell is no longer limited by the number of available paging channels, as it was assumed in previous works 11, 12. For configured groups such as fleets or VPNs, the assumption of a specific group identifier to reduce radio resource consumption at the physical level seems reasonable, and this can be used in the paging process.…”

“…In this section, firstly the well‐known optimum paging for individual users 5–6 is summarized in Section 3.1. Then, in Section 3.2 some group paging strategies based on the ideas of previous works 10–12 are presented and adapted to the considered scenario. Then, a hybrid approach combining concepts from both individual (minimizing individual paging cost) and group search (using a unique group identifier) is proposed in Section 3.3.…”

“…The problem of locating a group of users in a given number of steps, known as the conference call search problem has been already previously studied 10–12. Given a group of m users, located in a joint macro‐LA of n basic LAs (with ) of k cells each, there are certain probabilities of each of the m users being in a specific LA when a call is received.…”

“…Taking into account all these considerations, three different approaches, denoted as oblivious, semiadaptive and adaptive, can be evaluated 12: Oblivious: once a specific distribution of LAs in s PAs is performed, the search is carried out according to this distribution in the corresponding steps until all members of the group are found. The strategy is not notified of the location of a particular user, but only the moment in which all users are found.…”

“…Although there are some proposals to perform this group paging 10–12, they are mainly focused on a theoretical approach and have not been evaluated with simulations in a realistic cellular scenario. In this paper, the adaptive location management scheme presented in Ref.…”