From eyh5@ee.cornell.edu Wed Oct 24 20:36:29 2001 Return-Path: Received: from memphis.ece.cornell.edu (memphis.ece.cornell.edu [128.84.81.8]) by sundial.cs.cornell.edu (8.11.3/8.11.3/M-3.7) with ESMTP id f9P0aTo22544 for ; Wed, 24 Oct 2001 20:36:29 -0400 (EDT) Received: from james (james.ee.cornell.edu [128.84.236.65]) by memphis.ece.cornell.edu (8.11.6/8.11.2) with ESMTP id f9P0aqN06629 for ; Wed, 24 Oct 2001 20:36:52 -0400 Date: Wed, 24 Oct 2001 20:35:13 -0400 (EDT) From: Edward Hua To: egs@CS.Cornell.EDU Subject: 615 Paper # 46 Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Capacity of Ad Hoc Wireless Networks Jinyang Li, Charles Blake, Douglas S.J. De Couto, Hu Imm Lee, Robert Morris This paper aims to address the capacity in the ad hoc wireless networks. An a priori key assumption made is that the ad hoc network, although dynamic in nature, can be viewed as static when evaluating its capacity, since in most scenarios, nodes do not travel significant distances during packet transmissions. Although this assumption can be justified in this paper, not all scenarios of ad-hoc mobile networks may fit this criterion. Throughout the evaluations of ad hoc network capacity, the measurements are benchmarked against the single-hop throughput. Several conclusions are drawn from the analysis of ad hoc network capacity: 1)802.11 MAC is capable of sending at the optimal rate, but does not discover the optimum schedule of transmissions on its own. This inability is caused by the amount of competition the sender experiences, which prevents it from injecting more packets into the network. 2)An ideal ad hoc forwarding chain (i.e., a chain of forwarding nodes along the path) should be able to achieve one quarter of the throughput that a single-hop transmission can achieve. But the 802.11 MAC protocol is able to handle only one-seventh of the single-hop throughput. 3)When the network nodes are in an orderly fashion, carrying orderly traffic patterns, the 802.11 MAC protocol is more efficient, and the per-hope throughput remains relatively constant. On the other hand, in an environment of random node placement and random traffic pattern, as the path length increases, the bandwidth available for each node to originate packets decreases. One contribution given in the paper is that is provides a mathematical formula to calculate the expected path length between any source-destination pair in an ad hoc network. This length is influenced by two parameters: the locality index and the total area of the network coverage. This formula may be helpful in assisting the network designer to assess the optimal nodal placement and density in an ad hoc network. From wbell@CS.Cornell.EDU Wed Oct 24 22:06:50 2001 Return-Path: Received: from postoffice.mail.cornell.edu (postoffice.mail.cornell.edu [132.236.56.7]) by sundial.cs.cornell.edu (8.11.3/8.11.3/M-3.7) with ESMTP id f9P26no01929 for ; Wed, 24 Oct 2001 22:06:49 -0400 (EDT) Received: from [192.168.1.100] (syr-66-24-16-64.twcny.rr.com [66.24.16.64]) by postoffice.mail.cornell.edu (8.9.3/8.9.3) with ESMTP id WAA10649 for ; Wed, 24 Oct 2001 22:06:32 -0400 (EDT) Subject: 615 PAPER #46 From: Walter Bell To: egs@CS.Cornell.EDU Content-Type: text/plain Content-Transfer-Encoding: 7bit X-Mailer: Evolution/0.16.99+cvs.2001.10.18.15.19 (Preview Release) Date: 24 Oct 2001 22:06:10 -0400 Message-Id: <1003975600.1044.72.camel@brute> Mime-Version: 1.0 46) Capacity of Ad Hoc Wireless Networks This work presents a highly theoretical and math oriented analysis of the overall capacity of wireless networks. They analyze so called 'arbitrary' networks where nodes are randomly located in a disk of unit area in the plane and have an arbitrary destination to which they wish to send traffic at an arbitrary rate. They analyze situations in terms of the protocol model and the physical model, which are models for successful reception of a packet from a source to a destination. The protocol model simply says that the packet is received if the distance between source and destination is smaller than any other source sending to this destination, the packet is received. The physical model more closely models the physical layer and is represented by a distance fall off equation for the signal strength. Any signal received above a threshold is received. They show that under the protocol model, if each node has a transmission capacity of W, and all nodes are optimally places, the traffic pattern is optimal, and the range of transmission is optimal, a throughput of O(W\sqrt{n}) is achievable. They present the insight that wireless networks throughput decreases with the number of nodes if the communication distance increases with the number of nodes, therefore it is crucial to scalability to limit the number of hops communication must travel as the network grows. They also note that adding pure relay nodes to the network doesn't make the problem any better, as kn relays are added to the network, the throughput of the network only increases \sqrt{k+1} fold. This paper presents strong arguments that highly scalable ad-hoc networks are likely only possible given short communication distances and therefore compel routing algorithms to utilize this fact in improving protocols, as information about distant hosts is unlikely to be used in a successful large ad-hoc network. From papadp@ece.cornell.edu Thu Oct 25 10:12:45 2001 Return-Path: Received: from memphis.ece.cornell.edu (memphis.ece.cornell.edu [128.84.81.8]) by sundial.cs.cornell.edu (8.11.3/8.11.3/M-3.7) with ESMTP id f9PECio21965 for ; Thu, 25 Oct 2001 10:12:45 -0400 (EDT) Received: from hegel (hegel.ee.cornell.edu [128.84.236.63]) by memphis.ece.cornell.edu (8.11.6/8.11.2) with ESMTP id f9PED5N17422; Thu, 25 Oct 2001 10:13:05 -0400 Date: Thu, 25 Oct 2001 10:12:24 -0400 (EDT) From: "Panagiotis (Panos) Papadimitratos" X-Sender: papadp@hegel.ee.cornell.edu To: Emin Gun Sirer cc: Panagiotis Papadimitratos Subject: 615 PAPER 46 Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Review of "Capacity of Ad Hoc Wireless Networks," by J. Li, R. Morris et al. papadp@ece.cornell.edu Panagiotis Papadimtratos The authors examine the limitations imposed on ad hoc multihop topologies due to the use of a shared channel. They investigate the forwarding capability of a 802.11-based MANET without the presence of a routing protocol, which would simply impose additional tranmsission overhead. If the packet size of all traffic is assumed the same, then the presence of a routing protocol does not have a qualitative impact. First, a detailed study of the interactions between node transmissions is provided, over different types of topologies. The coupling of concurrent transmissions is shown through simulations for three different topologies: chain, sets of vertical/horizontal chains and grid. The theoreticaly (given the coupling) maximum throughput is not achieved by 802.11 under uniform load conditions. Nonetheless, it is approached when the pattern is randomized. This is the main contribution of this work: they provide an upper bound that incorporates the effect of the communication pattern on capacity, i.e., the achieved transmission rate per node. Their formulation under some assumptions matches the upper bound given by [Kumar] but with an arbitrary pdf (i.e., non uniform) modeling the communiation pattern, they indicate that the highest achievable throughput can exceed the O(1/sqrt(n)) bound. This is due to the locality of communication, and the reduced average path length leads to the increased achievable througput. An interesting point (not very well-supported though) is that the 'shortest path routing' (e.g., min-hop, or geographcal routing) is in accordance with the upper bound formulation, which seems to me that it brings route optimality back into the game. From daehyun@csl.cornell.edu Thu Oct 25 11:11:55 2001 Return-Path: Received: from wilkes.csl.cornell.edu (wilkes.csl.cornell.edu [132.236.71.69]) by sundial.cs.cornell.edu (8.11.3/8.11.3/M-3.7) with ESMTP id f9PFBto00068 for ; Thu, 25 Oct 2001 11:11:55 -0400 (EDT) Received: (from daehyun@localhost) by wilkes.csl.cornell.edu (8.9.3/8.9.2) id LAA11999 for egs@cs.cornell.edu; Thu, 25 Oct 2001 11:11:50 -0400 (EDT) (envelope-from daehyun) From: Daehyun Kim Message-Id: <200110251511.LAA11999@wilkes.csl.cornell.edu> Subject: 615 PAPER 46 To: egs@CS.Cornell.EDU Date: Thu, 25 Oct 2001 11:11:49 -0400 (EDT) X-Mailer: ELM [version 2.4ME+ PL54 (25)] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit This paper is a simulation/analysis study on the capacity of ad hoc wireless networks. They changed simulation parameters such as network size, traffic patterns and local radio interactions, and analyzed the results. They even validate some simulation results with experiments. This paper showed that the capacity of networks highly depends on the traffic pattern. If the distance between the source and the destination does not remain small, the capacity can not be scaled up with the network size. Therefore, the feasibility of large ad hoc networks is determined by the locality of traffic. In my opinion, the main contribution of this paper is that it analyzed the relationship between traffic pattern and network capacity. Other papers we have talked used very simple traffic patterns and did not pay attention to the network capacity much. But this paper showed this feature clearly, which can be used for the future protocol development. One think I'd like to point out is that this paper assumed static ad hoc network. Their reason for this assumption is that nodes do not move much during packet transit times. But, I think this might be over-simplified. As far as I know, any intensive study on the characteristics of ad hon network traffic has not be done yet. I think such studies should be done first, Before this kind of assumption is made. From jcb35@cornell.edu Thu Oct 25 11:34:34 2001 Return-Path: Received: from postoffice.mail.cornell.edu (postoffice.mail.cornell.edu [132.236.56.7]) by sundial.cs.cornell.edu (8.11.3/8.11.3/M-3.7) with ESMTP id f9PFYYo02940 for ; Thu, 25 Oct 2001 11:34:34 -0400 (EDT) Received: from localhost.localdomain (syr-66-66-30-147.twcny.rr.com [66.66.30.147]) by postoffice.mail.cornell.edu (8.9.3/8.9.3) with ESMTP id LAA12074 for ; Thu, 25 Oct 2001 11:34:33 -0400 (EDT) Received: from localhost (john@localhost) by localhost.localdomain (8.11.0/8.11.0) with ESMTP id f9PFbUL03923 for ; Thu, 25 Oct 2001 11:37:31 -0400 Date: Thu, 25 Oct 2001 11:37:29 -0400 (EDT) From: "John C. Bicket" To: egs@CS.Cornell.EDU Subject: 615 paper 46 Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII This paper further elaborates on the capacity on ad hoc wireless networks. Specifically, they look at how the traffic pattern determines the capacity of ad hoc networks, and indicated that large ad hoc networks are feasible if most of the communication is local. The first investigation this paper undertakes is the capacity of "chained" nodes, where each node is not mobile. They show that because a node's ability to send in 802.11 is affected by the amount of competition it experiences - a node can inject more packets into an network than the subsequent nodes can forward, and they get dropped as a result. The paper also considers how 802.11's back off performs poorly - They mention that a node may exponentially back off one of its timers when a RTS packet is corrupted by a hidden terminal. Next their analysis turns to lattice networks (ie chains but with 2 dimensions), and find the same problems as in the chain networks. They then evaluate how these results carry over into a graph with random traffic and random layout, where they determine that the capacity available to each node is explicitly dependent on the expected path length. They then find that with either bounded paths lengths or probabilistically short paths, ad hoc networks do not have unrealistically low capacity. comments: I would like to see some analysis in mobile environments, but I think that using a static network provides a good upper bound, and I thought it was a key insight that capacity depends on the locality of communication. From avneesh@csl.cornell.edu Thu Oct 25 11:57:03 2001 Return-Path: Received: from capricorn.ds.csl.cornell.edu (capricorn.csl.cornell.edu [132.236.71.92]) by sundial.cs.cornell.edu (8.11.3/8.11.3/M-3.7) with ESMTP id f9PFv3o06269 for ; Thu, 25 Oct 2001 11:57:03 -0400 (EDT) content-class: urn:content-classes:message Subject: 615 Paper 46 MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Date: Thu, 25 Oct 2001 11:58:19 -0400 Message-ID: <97C142C1212ED545B0023A177F5349C4053B04@capricorn.ds.csl.cornell.edu> X-MimeOLE: Produced By Microsoft Exchange V6.0.4712.0 X-MS-Has-Attach: X-MS-TNEF-Correlator: Thread-Topic: 615 Paper 46 Thread-Index: AcFdbd3pf86mURwLQjaUmr8RpEJ+aw== From: "Avneesh Bhatnagar" To: Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by sundial.cs.cornell.edu id f9PFv3o06269 Capacity of Wireless Networks. This paper evaluates a theoretical limit on the capacity of adhoc wireless networks. Two models are assumed: the arbitrary and random, but both in a static setting. The efficacy of MAC forwarding and 802.11 routing is evaluated under a horizontal flow and both horizontal and vertical grid flow model, thus establishing a upper and lower bound on the throughput possible and what kind of scheduling would enable this. Some results: a. 802.11 can send at the optimum rate but cannot find the right schedule. b. Throughput for a single chain is 1/7 insteafd of the expected 1/4. c. Increase in path length decreases available bandwidth. I think that since the paper was entirely theoretical, the authors have done a good job defining the upper and lower limits. However since my knowledge as to the basis of the assumpotions in these evaluations is limited, the only queries that I have are: a. Static model: It would be interesting to know why the paper takes this assumption and why could'nt a mobility model have been strapped onto these evaluations. b. There are horizontal and vertical chains that were considered for this study. Why could'nt any other model be chosen? From c.tavoularis@utoronto.ca Thu Oct 25 12:04:34 2001 Return-Path: Received: from bureau6.utcc.utoronto.ca (bureau6.utcc.utoronto.ca [128.100.132.16]) by sundial.cs.cornell.edu (8.11.3/8.11.3/M-3.7) with ESMTP id f9PG4Yo07456 for ; Thu, 25 Oct 2001 12:04:34 -0400 (EDT) Received: from webmail3.ns.utoronto.ca ([128.100.132.26] EHLO webmail3 ident: IDENT-NOT-QUERIED [port 64811]) by bureau6.utcc.utoronto.ca with ESMTP id <240592-28258>; Thu, 25 Oct 2001 12:04:18 -0400 Received: by webmail3.ns.utoronto.ca id <414676-224>; Thu, 25 Oct 2001 12:04:11 -0400 To: COM S 615 Subject: 615 PAPER 46 Message-ID: <1004025848.3bd837f8e5083@webmail.utoronto.ca> Date: Thu, 25 Oct 2001 12:04:08 -0400 (EDT) From: c.tavoularis@utoronto.ca MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit User-Agent: IMP/PHP IMAP webmail program 2.2.3 Scalability is a factor of network size, traffic patterns, local interaction and MAC layer interaction of the routing protocol. This paper addresses the effects of the MAC and routing layer interaction on ad hoc network capacity. It also determines the communication patterns that allow scalability. The authors consider a single shared channel and a static wireless network. The authors determine the network capacity limited only by the 802.11 MAC layer contention through a chain of nodes. A chain of nodes has ultimate throughput 1/3 since successive nodes must wait for each other to transmit, causing delays. Allowing interference further deteriorates performance due to collisions. Simulation results show even worse throughputs, down to 1/7 of 1.7Mbps. This decrease in performance is due to unfair contention since the source node has less contention than intermediate nodes (by symmetry) and therefore can ‘overload’ the forwarding nodes with traffic, while also delaying them from transmitting. The exponential backoff scheme in 802.11 is also disadvantageous since it results in periods of time when the channel is not being used. The authors then consider a square lattice network with horizontal and vertical traffic flows. Similar yet worse results are observed such that source nodes experience less contention than forwarding nodes, and exponential backoff periods are wasteful. In a random situation with predetermined routes (no routing protocol present), the throughput degrades even more, mainly due to areas of the network lacking in forwarding nodes. To study the capacity of an entire large network, the authors scale a network such that traffic increases with number of nodes and distance. Capacity is found to decrease with the length of the path and is therefore dependent on the traffic pattern. The most scalable traffic patterns occur when source destination pairs are within a local vicinity of each other. This also demonstrates the importance of choosing a shortest path when routing. The intuition is that ad hoc networks scale well because of spectral reuse, but increasing the number of nodes also increases forwarding load per node. In fact, ad hoc networks scale well when they behave as a set of overlapping sub- networks. Capacity of networks is an important issue, since it limits causes congestion, deteriorating performance. This study shows the importance of the MAC layer in routing, and demonstrates that 802.11 does not significantly hinder capacity. From viran@csl.cornell.edu Thu Oct 25 12:09:41 2001 Return-Path: Received: from moore.csl.cornell.edu (moore.csl.cornell.edu [132.236.71.83]) by sundial.cs.cornell.edu (8.11.3/8.11.3/M-3.7) with ESMTP id f9PG9fo08033 for ; Thu, 25 Oct 2001 12:09:41 -0400 (EDT) Received: from localhost (viran@localhost) by moore.csl.cornell.edu (8.11.3/8.9.2) with ESMTP id f9PG9ZD15774 for ; Thu, 25 Oct 2001 12:09:35 -0400 (EDT) (envelope-from viran@moore.csl.cornell.edu) X-Authentication-Warning: moore.csl.cornell.edu: viran owned process doing -bs Date: Thu, 25 Oct 2001 12:09:35 -0400 (EDT) From: "Virantha N. Ekanayake" To: Subject: 615 Paper 46 Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII This paper tries to simplify the results obtained in the earlier Gupta paper on capacity, in context of 802.11 and different traffic patterns. They show how the expected bandwidth isn't as bad as predicted by Gupta et al. as long as the traffic patterns are predominantly local. The paper was very clear, and had an excellent example of how inteference can affect the throughput of wireless networks. They also took into account how the 802.11 backoff scheme, and rts/cts signalling affects throughput. From teifel@csl.cornell.edu Thu Oct 25 12:22:23 2001 Return-Path: Received: from disney.csl.cornell.edu (disney.csl.cornell.edu [132.236.71.87]) by sundial.cs.cornell.edu (8.11.3/8.11.3/M-3.7) with ESMTP id f9PGMNo09668 for ; Thu, 25 Oct 2001 12:22:23 -0400 (EDT) Received: from localhost (teifel@localhost) by disney.csl.cornell.edu (8.11.3/8.9.2) with ESMTP id f9PGMH770651 for ; Thu, 25 Oct 2001 12:22:17 -0400 (EDT) (envelope-from teifel@disney.csl.cornell.edu) X-Authentication-Warning: disney.csl.cornell.edu: teifel owned process doing -bs Date: Thu, 25 Oct 2001 12:22:17 -0400 (EDT) From: "John R. Teifel" To: Subject: 615 PAPER 46 Message-ID: <20011025122138.G62337-100000@disney.csl.cornell.edu> MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Gupta & Kumar: This paper also discusses the capacity of wireless networks. It is a theory paper and quite frankly way too verbose and the writing style was almost unbearable. They show that every node in an ad hoc network must share channels with local neighbors in order for the total network capacity to be utilized. The throughput available to users tends towards zero as the number of users is increased, they suggest some type of clustering (i think) might be useful for maintaining throughput for users. They suggest that wireless networks may only be beneficial for networks with a small number of nodes--not very encouraging i suppose for ad hoc network visionaries. Adaptive or clustering may be able to overcome this or help in scalability. Essentially this paper said that ad hoc networks in their current implementation are limited and more complex schemes are needed in order for ad hoc networks to become practical. From andre@CS.Cornell.EDU Thu Oct 25 12:43:12 2001 Return-Path: Received: from postoffice.mail.cornell.edu (postoffice.mail.cornell.edu [132.236.56.7]) by sundial.cs.cornell.edu (8.11.3/8.11.3/M-3.7) with ESMTP id f9PGhBo12098; Thu, 25 Oct 2001 12:43:11 -0400 (EDT) Received: from khaffy (d7a046.dialup.cornell.edu [128.253.49.46]) by postoffice.mail.cornell.edu (8.9.3/8.9.3) with ESMTP id MAA25655; Thu, 25 Oct 2001 12:43:08 -0400 (EDT) Received: from andre by khaffy with local (Exim 3.31 #1 (Debian)) id 15wi0T-0000ZU-00; Thu, 25 Oct 2001 12:45:01 +0200 Date: Thu, 25 Oct 2001 12:45:01 +0200 From: =?iso-8859-1?Q?Andr=E9?= Allavena To: egs@CS.Cornell.EDU Cc: andre@CS.Cornell.EDU Subject: 615 PAPER 46 Message-ID: <20011025124501.A2144@khaffy> Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Disposition: inline Content-Transfer-Encoding: 8bit User-Agent: Mutt/1.3.20i Sender: =?iso-8859-1?Q?Andr=E9_Allavena?= Capacity of Ad Hoc Networks A very good paper, describing and poving in which cases an ad hoc network can work (scale) or not. The idea is to look at the capacity of a node (the amount of data a node an send) and compare it with the average length of a path. End to End througput is in O(1/sqrt(n)). They fisrt look at 802.11 which does not manage to achieve the theoretical maximum throughput in chain situations (the first node sends too much, the other ones wait for too much to gain access to the communication chanel). But overall the result is not too bad (1/7 instead of 1/4), closer to optimal in other situations. Scaling: Let C be the one hop capacity (how much a node sends to its neightboor, whether or not it was within a multihop path or not). C=kA=kn/d with A the surface, n the number of nodes and d the density C > nµL/r where L/r is the number of hops on the path (physical distance / radius of transmission) µ the packet rate then µ < (C/n) / (L/r) = (k/d)/ P P begin the avergae length of a path. _ P ~ sqrt(A) ~ sqrt(n) hence µ = O(1/sqrt(n)) Instead if you choose a power law for the neighbours instead of a random distribution, matching on the power exposant | x < -2 -> per node capacity constant (great!) | x = 2 -> per node capacity of O(1/log n) | -2 < x < -1 -> per node capacity of O(log(n)/sqrt(n)) | -2 < x -> per node capacity of O(1/sqrt(n)) Conclusion, stay with x<-2 if you want to scale (collection of superposed networks not using the links between them). -- André Allavena (local) 154 A Valentine Place École Centrale Paris (France) Ithaca NY 14850 USA Cornell University (NY) (permanent) 879 Route de Beausoleil PhD in Computer Science 06320 La Turbie FRANCE From samar@ece.cornell.edu Thu Oct 25 13:03:48 2001 Return-Path: Received: from memphis.ece.cornell.edu (memphis.ece.cornell.edu [128.84.81.8]) by sundial.cs.cornell.edu (8.11.3/8.11.3/M-3.7) with ESMTP id f9PH3lo14826 for ; Thu, 25 Oct 2001 13:03:47 -0400 (EDT) Received: from descartes (descartes.ee.cornell.edu [128.84.236.60]) by memphis.ece.cornell.edu (8.11.6/8.11.2) with ESMTP id f9PH47N22103 for ; Thu, 25 Oct 2001 13:04:07 -0400 Date: Thu, 25 Oct 2001 13:03:16 -0400 (EDT) From: Prince Samar X-Sender: samar@descartes.ee.cornell.edu To: egs@CS.Cornell.EDU Subject: 615 PAPER 46 Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII 46) Capacity of Ad hoc Wireless Networks This paper illustrates the capacity of wireless ad hoc networks over the 802.11 MAC layer using simulations and analysis. The article examines the limitations imposed by the use of a single shared channel over data forwarding and shows its effects on the network capacity and scalability. Various factors affecting the capacity, like network size, traffic patterns and local interactions, are studied alone and in combination. The authors examine different topologies: chains, sets of horizontal chains, grid and random topology. The authors conclude that the 802.11 is successful in determining reasonably good schedules. At the same time, they find that the simulated capacity is quite small in comparison to the optimal value. For example, for a chain topology, the ideal capacity is 1/4 and the simulated one is about 1/7. The paper shows that scalability of ad hoc networks is dependent on the locality of the communication pattern. Large networks are feasible only if the traffic is limited to the neighborhood of a node. The results in this paper reinforce the results in the Gupta and Kumar paper. It would be interesting to see how the results of the paper change when mobility is introduced.