Many-to-One Throughput Capacity of IEEE 802.11 Multihop Wireless Networks This paper investigates the many-to-one throughput capacity (and by symmetry, one-to-many throughput capacity) of IEEE 802.11 multihop networks, in which many sources send data to a sink. An example of a practical scenario is that of a multihop mesh network connecting source and relay nodes to an Internet gateway. In the trivial case where all source nodes are just one hop from the sink, the system throughput can approach L s , where L s is the throughput capacity of an isolated link consisting of just one transmitter and one receiver. In the nontrivial case where some source nodes are more than one hop away, one can still achieve a system throughput of L s by sacrificing and starving the non-one-hop source nodes-however, this degenerates to an unacceptable trivial solution. We could approach the problem by the following partitioning: preallocate some link capacity aL s ð0 a 1Þ at the sink to the one-hop source nodes and then determine the throughput for the source nodes that are two or more hops away based on the remaining capacity L ¼ ð1 À aÞL s . The throughput of the one-hop nodes will be around aL s . This paper investigates the extent to which the remaining capacity L can be used efficiently by the source traffic that is two or more hops away. We find that for such source traffic, a throughput of L is not achievable under 802.11. We introduce the notion of "canonical networks," a general class of regularly structured networks that allow us to investigate the system throughput by varying the distances between nodes and other operating parameters. When all links have equal length, we show that 2L=3 is the upper bound for general networks, including random topologies and canonical networks. When the links are allowed to have different lengths, we show that the throughput capacity of canonical networks has an analytical upper bound of 3L=4. The tightness of the bound is confirmed by simulations of 802.11 canonical networks, in which we obtain simulated throughputs of 0:74L when the source nodes are two hops away and 0:69L when the source nodes are many hops away. We conjecture that 3L=4 is also the upper bound for general networks. Our simulations show that 802.11 networks with random topologies operated with AODV routing typically achieve throughputs far below 3L=4. Fortunately, by properly selecting routes near the gateway (or by properly positioning the relay nodes leading to the gateway) to fashion after the structure of canonical networks, the throughput can be improved by more than 150 percent: indeed, in a dense network, deactivating some of the relay nodes near the sink can lead to a higher throughput. M ANY-TO-ONE communication is a common communication mode. In multihop wireless mesh networks (e.g., IEEE 802.11s network [1]), there is likely to be little traffic between client stations. Most clients would only want to connect to the core wired Internet via an Internet gateway, using relay nodes if necessary. The client stations and the Internet gateway form a many-to-one relationship. The placement of the relay nodes and the routing of traffic from the clients to the Internet gateway can affect the throughput significantly.. This paper investigates the many-to-one throughput capacity of IEEE 802.11 multihop networks. By symmetry, the throughput capacity thus found is also the same as that in a one-to-many scenario in which a source node generates multiple distinct data streams to be forwarded to their respective sinks (note that this is not to be confused with the multicast scenario in which the same data is to be forwarded to multiple sinks).. Gupta and Kumar [2] analyzed the capacity in the manyto-many situation. It provides the basic model that can be adapted for use in the analysis of the many-to-one communication. As a loose bound, it is obvious that the many-to-one throughput capacity is upper bounded by L s [2] , [3] , [4] , where L s is the single-link throughput capacity, since this is the rate at which the sink can receive data. There is a high probability, however, that the throughput capacity is lower than L s for a many-to-one network [4] . This paper follows the approach used in [2] , [3] , and [4] in characterizing which nodes can transmit together without packet collisions. The main difference is that here, we are interested in the throughput capacity obtained under the IEEE 802.11 distributed MAC protocol [5] . Specifically, we integrate into our analysis the effects of carrier sensing, the existence of an ACK frame for each DATA frame transmission, and the distributed nature of the CSMA protocol, while [2] , [3] , and [4] do not, and their bounds are obtained with the implicit assumption of perfectly scheduled transmissions.. One can in principle achieve the throughput capacity of L s in a many-to-one network by sacrificing and starving the source nodes that are more than one hop away from the sink. However, this degenerates to an unacceptable trivial solution with only the one-hop source nodes getting any throughput. We could approach the problem by the following partitioning: preallocate some link capacity aL s ð0 a 1Þ at the sink to the one-hop source nodes and then determine the throughput capacity for the source nodes that are two or more hops away based on the remaining capacity L ¼ ð1 À aÞL s . For example, the airtime at the sink could be partitioned so that one-hop traffic to the sink and multihop traffic to the sink do not use overlapped airtime. Since the one-hop source nodes do not need any relay, each unit of traffic consumes one unit of the link capacity of the sink. The throughput of the one-hop nodes will be around aL s . Because of the need for relay, each unit of source traffic that is two or more hops away in general consumes more than one unit of the link capacity of the sink. This paper investigates the extent to which the allocated capacity L can be used efficiently by the source traffic that is two or more hops away.. Indeed, based on the solution to the case where all source nodes are two or more hops away, one could turn around to determine the capacity to preallocate to the one-hop nodes to achieve fairness among nodes. For example, suppose that there are six sources nodes that are two or more hops away and that the throughput capacity for them is found to be 2L=3. Furthermore, suppose that there are three one-hop source nodes to which we would also like to allocate a throughput capacity of L=3 so that the ratio of allocations is 2 : 1 (in general, the allocation to the one-hop source nodes could be L for any ! 0 to achieve a ratio of 2=3 : ). Solving aL s ¼ L=3, L ¼ ð1 À aÞL s , gives L ¼ 3L s =4 and a ¼ 1=4. That is, one quarter of the link capacity at the sink should be preallocated to the one-hop source traffic.. This paper introduces the notion of "canonical networks," a general class of regularly structured networks that allows us to investigate the throughput capacity systematically by varying the distances between nodes and other operating parameters. There are three main contributions:. 1. When all links have equal length, we establish that the throughput capacity for 802.11 many-to-one networks is upper bounded by 2L=3 regardless of the network structure. The capacity achieved by canonical networks in simulation is 0:619L, which is close to 2L=3. When link lengths are allowed to vary, the throughput capacity of canonical networks can be upper bounded by 3L=4. We conjecture that this is also the upper bound for general networks. 2. Our studies of the canonical networks yield much insight on how a many-to-one network should be designed. Our simulations show that 802.11 networks with random topologies operated with AODV routing achieves throughputs far below the 3L=4 upper bound of canonical networks. As such, the popular AODV routing protocol is far from optimal for many-to-one communication. For the same random topology, an NP-hard optimization problem formulation yields a solution in which the selected routes near the sink form a structure resembling the canonical network. As a heuristic alternative to the NP-hard problem, routing or network design could be fashioned after the canonical network. Our investigation shows that a "manifold" canonical network structure near the center may yield a throughput improvement of more than 150 percent relative to that obtained by using AODV routing in general many-to-one networks with random topologies. Indeed, in a dense network, it is worthwhile to deactivate some of the relay nodes near the sink judiciously. 3. We find that ensuring that the many-to-one network is hidden-node free (HNF) leads to a higher throughput as compared to not doing so. This is in contrast to the many-to-many case, in which the large carrier-sensing range required to ensure the HNF property may lower the throughput due to the increased exposed-node (EN) problem [6] . This observation is used as a design principle in much of the study in 1 and 2 above. The rest of this paper is organized as follows: Section 2 provides the definitions and assumptions used in our analysis. Section 3 derives the throughput capacities of canonical networks and presents simulation results to support our findings. In addition, we demonstrate the desirability of the HNF property in many-to-one networks. Section 4 investigates general networks beyond the canonical network structure. We show that the routes selected by solving an NP-hard optimization problem form a structure near the center that resembles the optimal canonical network. We then apply this insight to demonstrate the desirability of designing the network according to a "manifold" canonical-network structure near the sink. Section 5 concludes this paper. In this paper, we have studied the throughput capacity of many-to-one multihop wireless networks based on the IEEE 802.11 MAC protocol. We focus on the nontrivial case where the source nodes are two or more hops away from the sink.. We have introduced a class of canonical networks whose throughput capacity can serve as a benchmark for general networks. We find that the throughput capacity of canonical networks under 802.11 is upper bounded by 3L=4, where L is the link capacity at the sink allocated to the traffic. If we restrict our attention to networks in which all links have the same length, the upper bound for throughput capacity is further reduced to 2L=3. The 2L=3 upper bound is a general upper bound for all networks (not just canonical networks) in which links have the same length.. For validation of our analytical results, we have conducted 802.11 network simulations. The results yield throughputs of around 0:69L (for variable-link-length canonical networks) and 0:62L (for equal-link-length canonical networks) under the worse case scenario when all non-one-hop source nodes are very far away and their traffic needs to go through many hops before reaching the sink node. That is, the simulated throughputs are reasonably close to the theoretical upper bounds of 3L=4 and 2L=3, respectively. This is quite a positive result considering the fact that 802.11 schedules transmissions in a rather random manner, while the examples we gave in Section 3.1 to achieve throughputs of 3L=4 and 2L=3 require very specific transmission orders.. We have considered both canonical networks with and without HNs. Our results indicate that HFDs yield higher throughput capacity. This is in contrast to the many-tomany case where HFD may not yield better throughputs [6] , [7] and may actually decrease the overall system throughput.. Building on our results on canonical networks, we have studied general networks: in particular, we examine how the results of general networks are related to those of canonical networks. For general networks, we put forth the concept of HFP for setting up routes to achieve a high throughput. Our experimental results indicate that the routes selected by the HFP algorithm resemble the structure of the canonical network near the sink. This gives rise to simple network design principles that attempt to approximate the canonical network structure. Specifically, we have shown that a manifold canonical network structure near the sink can yield a superior throughput that is more than 150 percent higher than that given by the popular AODV routing in a dense network. A key insight is that in a network densely populated with nodes, deliberating turning off some relay nodes in the area near the sink so as to approximate the canonical network structure can actually give rise to better throughput performance.. Yet another way to interpret our results is in terms of how to lay out relay nodes in a mesh network to relay traffic to the sink. In this scenario, relay nodes are part of the infrastructure of the mesh, and the source nodes are user nodes that can come and go. The relay structure is like a highway system, and it is desirable for it to resemble a canonical structure. The source traffic should get on the highway as soon as possible for further forwarding, perhaps using another frequency channel.

B O O O O O O O O O O O O B O O O O O B O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B I O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Large Deformation Diffeomorphic Metric Curve Mapping We present a matching criterion for curves and integrate it into the large deformation diffeomorphic metric mapping (LDDMM) scheme for computing an optimal transformation between two curves embedded in Euclidean space R d . Curves are first represented as vector-valued measures, which incorporate both location and the first order geometric structure of the curves. Then, a Hilbert space structure is imposed on the measures to build the norm for quantifying the closeness between two curves. We describe a discretized version of this, in which discrete sequences of points along the curve are represented by vector-valued functionals. This gives a convenient and practical way to define a matching functional for curves. We derive and implement the curve matching in the large deformation framework and demonstrate mapping results of curves in R 2 and R 3 . Behaviors of the curve mapping are discussed using 2D curves. The applications to shape classification is shown and J. Glaunès and A. Qiu contributed equally to this work.J. Glaunès MAP5, Matching curves embedded in R 2 and R 3 is important in the fields of medical imaging and computer vision (Zhang 1994; Besl and McKay 1992; Feldmar and Ayache 1996) . In medical imaging, the most striking gross morphological features of the cerebral cortex are the sulcal fissures on the cortical surface (Welker 1990 ). They are selected as the basis for structural analysis on the internal surface anatomy of the brain because they separate functionally distinct regions and provide a natural topographic partition of the anatomy. Even though major sulci consistently appear in all anatomies, they exhibit variability in size and configurations (Welker 1990) . A quantitative study of sulcal anatomical structures requires developing mathematical models for characterizing shape and geometry of curves, and for accommodating the variability present across populations (Durrleman et al. 2007; Fillard et al. 2007 ; Rettmann et al. 2002) . Moreover, image boundary, contours, and skeletons are often used to represent shapes of objects in many applications of computer vision, such as tracking human body motion in motion tracking, finding correspondence between maps and terrain images, object recognition and classification. All of these formulate two problems: representation of curves and mathematical models of transformations.. In non-rigid registration problems, desired transformations are often constrained to be diffeomorphic-one to one (invertible) and smooth with smooth inverse so that connected sets remain connected, disjoint sets remain disjoint, smoothness of features such as curves is preserved, and coordinates are transformed consistently. Consequently, many researchers have paid great attention to such diffeomorphic transformations particularly in the field of Computational Anatomy for studying the geometric variation of human anatomy (e.g. Grenander and Miller 1998; Gee and Bajcsy 1999; Miller et al. 2002; Twining et al. 2002; Beg et al. 2005; Joshi et al. 2004; Avants and Gee 2004; Thompson et al. 2004) .. Over the past several years we have been using large deformation diffeomorphic metric mapping (LDDMM) (Joshi and Miller 2000; Camion and Younes 2001; Beg et al. 2005) to map 3D volume coordinates in the brain as well as in the heart (Helm et al. 2006 ). This method not only provides a diffeomorphic correspondence φ between shapes C and S, but defines a metric distance in a shape space as well. The basic diffeomorphic metric mapping approach taken for understanding structures of object shapes is to place the set of objects into a metric space. The idea is to model the mapping of one from the other via a dynamic flow of diffeomorphisms (time dependent deformation) t ∈ [0, 1] of the ambient space R d . Instead of working directly in the space of diffeomorphisms, we work with time dependent vector fields, v t : R d → R d for t ∈ [0, 1], which model the infinitesimal efforts of the flow. The flow φ v t is then defined via the differential equation. with φ v 0 (x) = x, and the resulting diffeomorphism is given by the flow at time t = 1, φ v 1 . In order to ensure that the resulting solution to this equation is a diffeomorphism, v t must belong to a space, V , of regular vector fields (see Trouvé 1995; Dupuis et al. 1998 for specific requirements), for t ∈ [0, 1] with 1 0 v t V dt < ∞. V is a Hilbert space with an associated kernel function k V , and norm · V . This norm models the infinitesimal cost of the flow.. Assume that for any pair objects of C and S, there exists some vector fields v t such that the diffeomorphism φ v 1 transforms shape C to shape S, which we write φ v 1 · C = S. Then one can look at the optimal vector fieldsv t satisfying φv 1 · C = S and minimizing the integral of the infinitesimal costs. The metric distance between shapes, ρ(C, S), is defined as the length of the geodesic path φv t · C for t ∈ [0, 1] generated from C to S in the shape space. Such a metric between C and S has the form ρ(C, S) = inf . In practice, we often define an inexact matching problem: find a diffeomorphismφ t between two objects C and S as a minimizer of In this work we have proposed a mathematical framework in which both curves and their discrete samples are represented as vector-valued measures and embedded in a Hilbert space structure. Coupled with a model of deformations of the ambient space, we designed variational problems for curve matching takes convenient explicit formulations due to the use of the kernel of the Hilbert norm. We derived the case of the large deformations, given by integration of time-dependent vector fields. We also derived the case of the similitude transformation in Appendix B. We presented experiments for 2D and 3D curve mappings, and validated the accuracy of matching as well as demonstrated the behaviors of the curve mapping. Results indicate that the curve matching gives good matching and proper deformation fields compared to the landmark matching algorithm (Joshi and Miller 2000) . We also proposed to apply this technique for shape classification using the metric distances provided by the large deformation framework.. We consider kernels of the form k W (x, y) = h(|x − y| 2 ) and we note h x,y,i,j = h(|c. for any sequences of points x, y and indices i, j . We get. h z,y,q−1,j ·z q (τ z,q−1 · τ y,j ).. Hence the gradient of E with respect to z q is given by Fig. 15 Comparison of deformation fields between the landmark and curve matchings. Panels (a-d) show the target, source, deformed source surface after the landmark matching, deformed source surface after the curve matching. Red dots represents paired landmarks on the target and source surfaces. Panels (e-g) show triangulated meshes respectively corresponding to the surfaces in panels (b-d). (h z,y,q−1,j − h z,y,q,j )τ y,j. Appendix B: Similarity Transformation In our experiments, we first used the similarity transformation to transform curves into the same orientation and scale, as described in Appendix B. Then, we applied the curve matching under the LDDMM setting to deform one curve to the other. Kernels of k V (x, y) and k W (x, y) were radial with the form e We used a conjugate gradient routine to perform the minimization of functional J in (18) with respect to variables α i (t) . Of course any other optimization scheme could be considered at this point. The different steps required to compute the functional and its gradient for each iteration are the following:

B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Estimating the Relative Contribution of dNTP Pool Imbalance and APOBEC3G/3F Editing to HIV Evolution In Vivo The human immunodeficiency virus (HIV) has a genome that is rich in adenine, and its rapid evolution shows an observed bias of guanine (G) to adenine (A) mutations. Two mechanisms have been proposed to explain these properties: (1) an imbalance in dNTP pool concentrations which drives the misincorporation process during reverse transcription, and (2) cytidine deamination by the APOBEC3G/3F restriction factor, causing G to A mutations most notably in specific dinucleotide contexts. Although crucial to understanding HIV evolution, current estimates on misincorporation bias during the replication cycle are based on scarce in vitro measurements. In this work, HIV partial pol sequences obtained for drug resistance testing purposes are analyzed using likelihood methods to estimate various models of HIV misincorporation bias in vivo. The technique is robust to selection on the amino acid sequence and selection against CpG dinucleotides. A model where misincorporations are explained only by an imbalance in dNTP pool concentrations, together with a preference for transitions versus transversions, explained 98% (95% confidence interval [C.I.] 93-100) of the observed variation in freely estimated misincorporation rates. Although dinucleotide context was responsible for variation in misincorporation probabilities, this variation was not specific for G to A mutations implying that the footprint of APOBEC3G/3F editing could not be detected. These results indicate that an imbalance in dNTP pool concentrations explains most of the bias in HIV nucleotide misincorporations, while the effect of editing by APOBEC3G/3F on HIV evolution, based on its dinucleotide specificity, could not be observed in this study. T HE RAPID EVOLUTION of the human immunodeficiency virus (HIV) is caused by a rapid turnover of the large intra-host population with a high mutation rate per generation. This is a major obstacle for designing effective therapeutic strategies (Rambaut et al., 2004) as it has caused a large genetic diversity in the HIV pandemic, complicating vaccine design, and as it causes drug resistance to evolve quickly during antiviral therapy.. Evolution can be considered as a two-step process of misincorporation followed by selection. For example in the context of evolution of antiviral drug resistance within a HIV-infected patient, the rate at which resistance mutations are expected to appear depends on the probability of generating the required nucleotide mutations (van de Vijver et al., 2006) , as well as on the fitness gain of these amino acid mutations in presence of treatment.. HIV is a retrovirus that encodes its genomic information as diploid single stranded RNA (ssRNA), which is copied during the replication process by the viral reverse transcriptase (RT) to ds-cDNA and integrated in the host genome. Subsequently, the proviral DNA is transcribed by the host RNA pol II into messenger ssRNA, which is used as a template for protein translation or serves as the RNA genome in new virus particles. The high mutation rate can be partly explained by the the negligible proof reading capability of the two enzymes involved (O'Neil et al., 2002) , leading to many misincorporations during the replication process. While G ! A has been described as the most frequently observed substitution (Vartanian et al., 1994) , no reliable quantitative estimates exist for the 12 different misincorporation probabilities. Current estimates have been drawn from scarce in vitro measurements of the fidelity during the HIV replication cycle, mainly from the study by Mansky and Temin (1995) . In this study, only 42 nucleotide changes were observed in total and some mutations were even not observed, leading to rather unreliable esimates of the 12 probabilities. Furthermore, the in vitro infidelity of replication may not be representative for the in vivo environment, for example due to a potentially different composition of the in vivo dNTP pools (Jamburuthugoda et al., 2006) , which are affected by cell metabolism and transcriptional activity.. Like many lentiviruses, HIV has an unusual genome nucleotide composition that is highly rich in adenine, but poor in guanine or cytosine (Berkhout and Hemert, 1994) . Besides intrinsic properties of the RT and RNA pol II enzymes, which may cause a bias in their misincorporation rates, two hypotheses have been proposed to explain the adenine richness of lentiviral genomes, in view of the large number of G ! A substitutions. On the one hand, an imbalance in intracellular dNTP concentrations, with in particular a low amount of dCTP and high amount of dTTP, was suggested to cause frequent misincorporation by RT of dTTP instead of dCTP in the minus strand, resulting in a G ! A mutation in the plus strand (Vartanian et al., 1994; Balzarini et al., 2001) . On the other hand, the cellular proteins APOBEC3G/3F have been shown to cause long stretches of G ! A hypermutation in the HIV genome and is assumed to act as an antiviral defense mechanism (Lecossier et al., 2003) . These enzymes are sensitive to the nucleotide context to carry out their editing, and cause preferentially GpA ! ApA and GpG ! ApG mutations.. Our work stems from the need for an accurate estimate of the misincorporation rates, to reverse engineer the fitness impact of observed patterns of substitutions during treatment (Deforche et al., 2007) . We present a new likelihood-based computational method to estimate relative misincorporation rates from substitutions in a protein coding gene region, under the assumption that selection acts mostly on the amino acids, and against CpG dinucleotides (Shpaer and Mullins, 1990) . We use the method to estimate several models of HIV-1 misincorporation probabilities from a large set of longitudinal pol population sequences collected for antiviral resistance testing. We estimated several models of HIV misincorporation rate bias from in vivo data. Unlike substitutions, which may be observed directly in offspring, or estimated using phylogenetic methods from a crosssectional sample of a population, generated mutations are not proportionally observed in offspring due to selection and little is known about biases in their generation. The presented method uses observed substitutions in genomic regions that code for proteins, and is robust to the selective pressures that acts on the amino acid sequence level, by only observing preferences between mutations that are equivalent on the FIG. 4 . Misincorporation rate variation depending on the downstream nucleotide. For each mutation X , we compare the free misincorporation rate estimate (X ! Y ) with the four estimates depending on the downstream nucleotide (X pA, X pC, X pG, X pT) taken from a free-dinucleotide model for that base (four right bars). amino acid sequence, since they generate the same amino acid sequence. The method is not confounded by hitchhiking effects where a substitution is fixed by a positive selection of a mutation on a different position in the the same strain, or by sequential evolution at multiple codons, because the method infers from an observed bias for a particular substitution over other substitutions that would have had exactly the same effect on the amino acid sequence, including at intermediate time points.. The method generates accurate estimates of misincorporation bias only when selection acts solely on the amino acid sequence. However, selection against CpG dinucleotides in HIV is both observed and its mechanism well understood (Shpaer and Mullins, 1990 ). Therefore we attempted to correct for this effect in a pragmatic way by including a factor that modifies the rate when a CpG dinucleotide is added or removed by the mutation. While estimates of these factors indeed show a consistent correction, the selection against CpG dinucleotides competes with selection on the amino acid sequence (unless for neutral mutations), and therefore is not necesarilly uniform for all mutations. This may explain why in Figure 4 estimated rates dependent on the downstream nucleotide still reveal variation involving CpG (such as deflated rates for TpG ! CpG and inflated rates for CpG ! ApG and CpG ! TpG), although this was corrected for using two general factors. We did not consider other factors that provide selective pressure directly on the nucleotide sequence, such as selection to preserve RNA secondary structure which has been described for certain transcriptional areas in the HIV genome (Hofacker et al., 2004) .. Our findings suggest a general tendency against misincorporation of a base instead of adenine (A ! Y mutation), and at the same time the tendency towards misincorporation of adenine instead of any other base (X ! A mutation; Fig. 3 ). The latter was not solely caused by the often cited G ! A transition, but also by C ! A and T ! A which were the most frequent transversions (Fig. 2) . This finding is compatible with the hypothesis that imbalance in dNTP pools is the mechanism that has shaped the observed genome nucleotide composition of HIV-1, as this would explain the observed symmetry between fidelity and misincorporation for each base: higher abundance of a specific dNTP would cause both the higher fidelity in copying and higher tendency of misincorporation of the corresponding base. To verify this hypothesis, we estimated a dNTP model, which assumed that misincorporations were solely caused by an imbalance in dNTP concentrations with a bias towards transitions. Since our method cannot distinguish between mutations that are generated during the minus or plus strand synthesis, we modelled only misincorporations during plus strand synthesis. Rates obtained in this way explained most of the variation observed in the free estimates, and thus confirm that dNTP pool concentrations may indeed be the source for misincorporation during the reverse transcription process. The estimated relative concentrations of dNTPs in Table 1 should not be interpreted as biological estimates, since they depend critically on the model assumption that all misincorporations are generated during plus strand synthesis. For example, if we instead had assumed that they are all generated during minus strand synthesis, the values would have been swapped with their complement (dCTP $ dGTP, and dATP $ dTTP). The dNTP model explains the observation that G ! A is the most frequently estimated misincorporation (and most observed substitution) as a consequence of the fact that it is the only transition towards adenine.. Because APOBEC3G/3F causes mostly GpA ! ApA and GpG ! ApG mutations, we investigated dependence of the misincorporation rate on the downstream nucleotide (Fig. 4) . We discovered considerable variation for all mutations with respect to the downstream nucleotide, which suggests either a true dinucleotide context-dependent generation or context-dependent selection on the nucleotide sequence which confounds the analysis, or both. Variation for G ! A with respect to the downstream nucleotide was not more pronounced than variation for other mutations. Other context-dependent influences on the misincorporation of other mutations appear to have a larger effect than the effect APOBEC3G/3F possibly may have on the G ! A mutation rate, and it cannot be excluded or confirmed that there is any effect of APOBEC3G/3F at all.. A comparison of the equilibrium frequencies of the four bases implied by the misincorporation matrix of the free model, with observed frequencies of the four bases in HIV isolates, implies that a further enrichment of the viral genome towards more adenine is still possible and perhaps ongoing unless the genome has already reached an equilibrium where selection balances this intrinsic bias in misincorporation.. Computational methods to reconstruct the phylogeny from a nucleotide sequence alignment usually co-estimate a nucleotide substitution rate model. Estimated substitution rates are inherently influenced by selection. However, the third codon position is degenerate for many amino acids and substitutions at this position are more likely to be synonymous. Therefore, analyses which are confounded by selection are frequently done using data from the third codon position only. However, substitution rates estimated from a third codon position will be strongly biased towards those substitutions (mostly transitions) which are synonymous, and thus also cannot be used to reliably estimate misincorporation rates. Codon substitution models consider the entire codon as a single state, and provide in this way information on preference for a specific nucleotide substitution over other equivalent substitutions (those that generate the same amino acid). Therefore, the described technique could in principle be adapted to such a model to estimate misincorporation rates. This could be useful for comparative analyses among different viruses or other organisms.. In summary, we presented a computational method to estimate misincorporation rates from substitutions. We applied the method to estimate several models for misincorporation during the HIV replication cycle, from which we could conclude that imbalance in dNTP concentrations provide a reasonable explanation for the estimated bias in misincorporation rates. We believe the estimated misincorporation models will be useful for modelling virus evolution in forward-time simulators, for example to predict evolution of drug resistance and treatment response, or to model the process of CTL escape. A method is presented to estimate misincorporation rates from observed substitutions in serially sampled sequences (Fig. 1) . Nucleotide substitutions were considered equivalent when they had exactly the same effect at the amino acid level, i.e., either changing to the same amino acid or both a silent substitution. The observed nucleotide substition was considered only against alternative equivalent substitutions. Because selection is assumed to act on phenotypic changes at the amino acid level, and is therefore blind for equivalent substitutions, the method was robust with respect to selection at the amino acid level. Each observed substitution in a codon at which only a single nucleotide substitution was observed, was considered as the outcome of a probabilistic experiment with probabilities proportional to the misincorporation rates of each of the equivalent substitutions. A misincorporation model is then estimated by applying this process for many observed nucleotide substitutions in a maximum likelihood or Markov Chain Monte Carlo framework.. Several models for HIV-1 in vivo misincorporation rates were estimated using 5164 partial pol population sequence pairs, obtained for resistance testing.. A first model allowed unrestricted estimates of the misincorporation rates (model free in Fig. 2) . A large variation is observed: the most frequent mutation (G to A) is approximately 30 times more probable than the least frequent mutation (C to G). In general, transitions were more frequent than transversions. The most common transversions were C ! A and T ! A. When combining rates per template base, we obtain FIG. 2. Maximum likelihood estimates of relative HIV misincorporation rates estimated with two models from observed in vivo substitutions, cancelling for selection on the amino acid sequence, and including correction for selection against CpG dinucleotides. The free model allows unrestricted estimates of the misincorporation rates, while the dNTP model allows variation only based on dNTP concentrations with a bias for transitions. n, number of degrees of freedom.. the estimated fidelity of maintaining the correct bases in the HIV-1 genome template during one replication cycle (Fig. 3, left) . When combining rates per misincorporated base, we obtain the bias in mutation towards each of the four bases (Fig. 3, right) . A striking symmetry may be observed between fidelity for maintaining a base and mutation for that base (Pearson correlation: R 2 D 0:94OE0:02 1:00; p D 0:03). Most notably, adenine was at the same time the base most reliably maintained during a replication cycle, and most frequently mutated to.. In a dNTP model, we let the mutation rate X ! Y to be proportional to the concentration of the misincorporated base, and inversionally proportional to the concentration of the correct base, with a preference for transitions (model dNTP in Fig. 2) . In this way, the model forces the symmetry that was observed between fidelity for maintaining a base and mutation for that base in the free model. Although this model (n D 6) has 7 degrees of freedom less than the free model (n D 13), it can explain most of the estimated variation in misincorporation rates (Pearson correlation, R 2 D 0:98OE0:93 1:00; p < 10 9 ). Nevertheless, a comparison of the two models using AIC indicates that the free model (AIC D 44909) is still preferred over the dNTP model (AIC D 45460). Table 1 shows the estimates for the parameters in the dNTP model. To investigate variation in estimated misincorporation rates, depending on the downstream nucleotide, we estimated 12 models corresponding to every mutation X ! Y where we allowed independent estimates of the probability of that misincorporation for every downstream nucleotide (Fig. 4) . For every mutation, substantial variation in misincorporation probability was found depending on the downstream nucleotide.. All estimated models include two parameters to correct for known selection against CpG dinucleotides. Estimates for these parameters were similar for all models and confirmed a bias against CpG dinucleotides in the genome. In the free model, estimates for these parameters were CpG C D 0.55 (0.50-0.60) and CpG D 1.43 (1.29-1.59).. If no selection would counter balance the effect of misincorporation, then the misincorporation rate matrix Q estimated by the free model (Fig. 2)

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Filtered and recovering beam search algorithms for the early/tardy scheduling problem with no idle time In this paper we consider the single machine earliness/tardiness scheduling problem with no idle time. We present heuristic algorithms based on the filtered and recovering beam search techniques and compare them with existing neighbourhood search and dispatch rule heuristics. Filtering procedures using both priority evaluation functions and problem-specific properties have been considered. Extensive preliminary tests were performed to determine appropriate parameter values for the beam search algorithms and the neighbourhood search procedure.The computational results show that the recovering beam search algorithms outperform their filtered counterparts in both solution quality and computational requirements, while the priority-based filtering procedure proves superior to the rules-based alternative.The best solutions are given by the neighbourhood search algorithm, but this procedure is computationally intensive and can therefore only be applied to small or medium size instances. The recovering beam search heuristic provides results that are close in solution quality and is significantly faster, so it can be used to solve even large instances.Keywords: scheduling, early/tardy, beam search, heuristics Resumo 1 Neste artigo consideramos um problema de sequenciamento com um único processador, custos de posse e atraso e inexistência de tempo morto. Heurísticas baseadas nas técni-cas de filtered e recovering beam search são apresentadas e comparadas com algoritmos de pesquisa local e dispatch rules existentes. Dois diferentes tipos de procedimentos de filtragem -funções prioridade e regras relativas ao problema em causa -são estudados.Diversos testes computacionais foram efectuados para determinar valores apropriados para os parâmetros usados pelos diversos algoritmos.Os testes computationais mostram que os procedimentos de recovering beam search superam os algoritmos baseados em filtered beam search não só na qualidade da solução obtida, como também no tempo de computação. O método de filtragem qua utiliza funções prioridade revelou-se substancialmente melhor do que o baseado em regras. O algoritmo de pesquisa local proporcionou os melhores resultados, mas apenas pode ser aplicado a instâncias de dimensão pequena ou média, em virtude dos seus elevados requisitos computacionais. A heurística de recovering beam search gera soluções com uma qualidade bastante próxima e o seu tempo de computação é substancialmente inferior, pelo que pode ser utilizada para resolver instâncias de dimensão elevada.Palavras-chave: sequenciamento, custos de posse e atraso, beam search, heurísticas We consider a single machine scheduling problem with earliness and tardiness costs that can be stated as follows. A set of n independent jobs {J 1 , J 2 , · · · , J n } has to be scheduled without preemptions on a single machine that can handle at most one job at a time. The machine and the jobs are assumed to be continuously available from time zero onwards and machine idle time is not allowed. Job J j , j = 1, 2, · · · , n, requires a processing time p j and should ideally be completed on its due date d j . For any given schedule, the earliness and tardiness of J j can be respectively defined as E j = max {0, d j − C j } and T j = max {0, C j − d j }, where C j is the completion time of J j . The objective is then to find a schedule that minimizes the sum of the earliness and tardiness costs of all jobs P n j=1 (h j E j + w j T j ), where h j and w j are the earliness and tardiness penalties of job J j .. The inclusion of both earliness and tardiness costs in the objective function is compatible with the philosophy of just-in-time production, which emphasizes producing goods only when they are needed. The early cost may represent the cost of completing a project early in PERT-CPM analyses, deterioration in the production 2 of perishable goods or a holding cost for finished goods. The tardy cost can represent rush shipping costs, lost sales and loss of goodwill. The assumption that no machine idle time is allowed reflects a production setting where the cost of machine idleness is higher than the early cost incurred by completing any job before its due date, or the capacity of the machine is limited when compared with its demand, so that the machine must be kept running.. As a generalization of weighted tardiness scheduling [5] , the problem is strongly NP-hard. A large number of papers consider scheduling problems with both earliness and tardiness costs. We will only review those papers that examine a problem that is exactly the same as ours. For more information on earliness and tardiness scheduling, interested readers are referred to Baker and Scudder [2] , who provide an excellent review.. Ow and Morton [9] developed several early/tardy dispatch rules and a filtered beam search procedure. The early/tardy dispatch rules clearly outperformed known heuristics that ignored the earliness costs, but were still far from optimal, while the filtered beam search procedure provided very good solutions for small or medium size problems, but required excessive computation times for larger problems. Valente and Alves [14] considered the best dispatch heuristic of Ow and Morton and proposed an additional dispatch rule and a greedy procedure. They presented functions for determining the value of a lookahead parameter used by both dispatch rules, and also considered the use of dominance rules to further improve the schedule obtained by the heuristics. A neighbourhood search algorithm was presented by Li [6] . Exact approaches have also been proposed, and branch-and-bound algorithms were presented by Abdul-Razaq and Potts [1] , Li [6] and Liaw [7] . The lower bounding procedure of Abdul-Razaq and Potts was based on the subgradient optimization approach and the dynamic programming state-space relaxation technique, while Li and Liaw used Lagrangean relaxation and the multiplier adjustment method. Valente and Alves [15] show that using better initial sequences can improve the lower bounds developed by Li and Liaw. In this paper we consider heuristic algorithms based on both the filtered and the recovering beam search approaches. These algorithms are compared with the best existing dispatch rule and the neighbourhood search procedure proposed by Li [6] . We have considered filtering procedures using both priority evaluation functions and problem-specific properties. Extensive computational tests were performed to determine the parameter values that provided the best balance between solution quality and computational effort for the beam search algorithms and the neighbourhood search heuristic. We also consider using some dominance rules to improve the solutions obtained by the heuristics.. The remainder of the paper is organized as follows. In section 2 we describe the beam search approach and its several variations. The proposed algorithms and the choices made for their main components are presented in section 3. The computational results are reported in section 4 and some concluding remarks are given in section 5. In this paper we considered the single machine scheduling problem with earliness and tardiness penalties and no idle time. We presented heuristic algorithms based on the filtered and recovering beam search techniques and compared them with existing neighbourhood search and dispatch rule heuristics. A filtering procedure is required by the filtered and recovering beam search algorithms. We have considered filtering procedures using both priority evaluation functions and problem-specific properties. The beam search algorithms and the neighbourhood search heuristic use several parameters whose value must be specified. We performed extensive computational tests to determine the parameter values that provided the best balance between solution quality and computational effort. The use of some dominance rules to improve the solutions obtained by the heuristics was also considered. The computational results show that the dominance rules can improve the solution quality with little additional computational effort, and their use is therefore recommended. The algorithms with a priority evaluation function filtering procedure outperform their rules-based counterparts in solution quality. The recovering beam search procedures are clearly superior to the filtered beam search alternatives, since they not only provide better solutions, but are also faster. The best results are given by the NSearch heuristic, but this algorithm is computationally demanding and can be applied only to small or medium size instances. The RBS_P procedure provides results that are close to the best in solution quality and is significantly faster. Therefore, this procedure is then the heuristic of choice for medium and even large size problems. The performance of the recovering beam search algorithm was quite adequate, and this heuristic approach seems to strike a good balance between solution quality and computational efficiency. These results confirm the potential of the recently introduced recovering beam search technique, and as a possible step for future research it certainly seems worthy to investigate its behaviour on other problems.

O O O B I O O O B B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B I O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B B B I B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O B I O O B O O O O O B O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O


Analysis of reactive scheduling problems in a job shop environment In this paper, we study the reactive scheduling problems in a stochastic manufacturing environment. Speci®cally, we test the several scheduling policies under machine breakdowns in a classical job shop system. In addition, we measure the eect of system size and type of work allocation (uniform and bottleneck) on the system performance. The performance of the system is measured for the mean tardiness and makespan criteria. We also investigate a partial scheduling scheme under both deterministic and stochastic environments for several system con®gurations. Ó Scheduling is an important element of production systems because it serves as an overall plan on which many other shop activities are based. By properly planning and timing of shop oor activities, various system performance measures can be optimized. There are two key elements in any scheduling system: schedule generation, and revisions (monitoring and updating the schedule). The ®rst element which acts as a predictive mechanism determines planned start and completion times of operations of the jobs.. The second element which is viewed as the reactive part of the system monitors the execution of the schedule and copes with unexpected events (i.e., machine breakdowns, tool failures, order cancelation, due date changes, etc).. The major criticism brought against the predictive mechanisms in practice is that the actual events on the shop¯oor can be considerably different compared to the one speci®ed in the schedule due to the random interruptions (i.e., breakdowns, scraps, due date changes, order cancelations, etc.). Thus an appropriate corrective action (or response) should be taken to improve the performance of the degraded schedule. Beside other environmental factors, the nature of a response depends on the way that a schedule is generated (or types of scheduling decisions are made). In the scheduling literature, there are two European Journal of Operational Research 126 (2000) 567±586 www.elsevier.com/locate/dsw main scheduling approaches: o-line scheduling in which all available jobs are scheduled all at once for the entire planning horizon and on-line scheduling in which scheduling decisions are made one at a time when needed. In the on-line approach, the schedule is not determined in advance, but it is constructed over time as the system state changes. Thus, any disturbance can automatically be handled by this event based scheduling system. In the o-line approach, however, there is an a priori generated (predictive) schedule which needs to be revised whenever necessary. These revisions can be performed in several ways, ranging from repair of the existing schedule to generating a new schedule.. In this study, we develop and compare several such schedule revision techniques. Generally speaking, schedules are easily generated by using on-line dispatching rules. But the solution quality is sacri®ced due to the myopic nature of these rules. On the other hand, the optimum seeking o-line approaches search in a larger solution space and hence generate high quality schedules at a cost of greater computation times. One of the objectives of this study is to compare these two scheduling methods (i.e., simple heuristic vs more sophisticated optimum seeking method) so that we get some insights into their relative strengths and weaknesses in dierent environmental conditions.. In general, the majority of the published works in the scheduling area deals with the task of schedule generation. The second part (reactive element) has not been studied well in the literature. In this context, this paper provides an important contribution towards the analysis and better understanding of the reactive scheduling problems.. Another point is that a system with a larger number of machines and jobs is more complex and thus the scheduling problems are more dicult than small systems. However, it is not generally known in the literature how the relative performance of the scheduling methods is aected by this system size factor. In addition, we suspect that the work load distribution in the system (uniform loading vs nonuniform loading or bottleneck system) may also aect the relative performance of scheduling systems. One can intuitively expect better scheduling decisions in the uniform system (long-term utilization of machines are nearly the same) than that of the nonuniform system. However, how these two schedule generation methods (o-line vs on-line) perform in such manufacturing environments is again an open research question. Finally, there is a need to compare the scheduling methods under stochastic disturbances so that we assess their strengths and weaknesses.. The purpose of this paper is to investigate all these issues stated above. Speci®cally, we analyze the eects of the load allocation (bottleneck vs uniform), system complexity (small vs large), and stochasticity (breakdowns vs not) on the performance of the on-line and o-line scheduling methods. Moreover, we develop and compare several reactive policies. We also investigate the feasibility of using partial scheduling in both deterministic and stochastic environments.. The rest of the paper is organized as follows. We present a literature review in Section 2. This is followed by the discussion on system considerations and experimental conditions in Section 3. In Section 4, the scheduling methods are compared in deterministic and stochastic environments. In Section 5, we investigate a periodic response scheduling policy. We then study partial scheduling in Section 5.2. Finally, we make concluding remarks in Section 6. In this paper, we studied the reactive scheduling problems and measure the eect of shop¯oor con®gurations (system size and load allocation) on the performance of scheduling methods (o-line and on-line scheduling methods). We also examine the eectiveness of partial scheduling in stochastic manufacturing environment. The following conclusions are drawn from this study:. First, we observe that the relative performances of the scheduling methods are not seriously affected by the systems size (i.e., system being big or small), but rather they are more aected by the system load (i.e., system being congested or not).. Second, we note that distribution of the load in the system have signi®cant impact on the performance of the scheduling methods. Speci®cally, the optimization based o-line scheduling method performs better than on-line dispatching rules when the load across the machines are not uniform (i.e, there are bottleneck and/or underutilized machines in the system). These two observations also hold in stochastic environment. Third, the o-line scheduling method is aected more than the on-line dispatching mechanisms when there is stochastic disturbances such as machine breakdowns. This is consistent with the previous studies (Lawrence and Sewell, 1997; Sabuncuoglu and Karabuk, 1997 ) that the performance of optimization methods and simple heuristics get close to each other when there is considerable uncertainty and variability in the system.. Fourth, under the stochastic disturbances the performance of the o-line scheduling method improves as the level scheduling frequency increases. But the marginal improvement is not signi®cant for the high levels of scheduling frequency. The results also indicate that frequent scheduling (i.e., high level scheduling frequency) is more effective in the large systems with uniform load across the machines.. Fifth, partial scheduling with optimization based scheduling algorithms can be a very practical scheduling tool in a highly dynamic and stochastic environment. Even though the performance of the schedule can be inversely affected by the extra amount of inserted idle times and myopic characteristics of the partial scheduling decisions, the amount of deterioration in the schedule is not always very signi®cant. Besides, the potential saving in CPU times is great when the partial scheduling can be employed. These observations are for each scheduling criteria under both uniform and nonuniform (i.e., bottleneck) system regardless of the system size.. We ®nally note that more research is needed in this area. An immediate extension would be testing the results of this paper under the dynamic job shop environment with various random disturbances. Another further research direction would be to investigate new schedule revision techniques together with considerations of the partial scheduling.

O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O