### Collaboration and Multitasking in Networks: Architectures, Bottlenecks and Capacity

"... Motivated by the trend towards more collaboration in work flows, we study networks where some activ-ities require the simultaneous processing by multiple types of multitasking human resources. Collaboration imposes constraints on the capacity of the process because multitasking resources have to be ..."

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Motivated by the trend towards more collaboration in work flows, we study networks where some activ-ities require the simultaneous processing by multiple types of multitasking human resources. Collaboration imposes constraints on the capacity of the process because multitasking resources have to be simultaneously at the right place. We introduce the notions of collaboration architecture and unavoidable bottleneck idle-ness (UBI) to study the maximal throughput or capacity of such networks. Collaboration and multitasking introduce synchronization requirements that may inflict unavoidable idleness of the bottleneck resources: even when the network is continuously busy (processing at capacity), bottleneck resources can never be fully utilized. The conventional approach that equates network capacity with bottleneck capacity is then incorrect because the network capacity is below that of the bottlenecks. In fact, the gap between the two can grow linearly with the number of collaborative activities. Our main result is that networks with nested collaboration architectures have no unavoidable bottleneck idleness. Then, regardless of the processing times of the various activities, the standard bottleneck procedure correctly identifies the network capacity. We also prove necessity in the sense that, for any non-nested architecture, there are values of processing times for which unavoidable idleness persists. The fundamental tradeoff between collaboration and capacity does not disappear in multi-server networks and has important ramifications to service-system staffing. Yet, even in multi-server networks, a nested collaboration architecture still guarantees that the bottleneck capacity is achievable. Finally, simultaneous collaboration, as a process constraint, may limit the benefits of flexibility. We study the interplay of flexibility and unavoidable idleness and offer remedies derived from collaboration architectures.

### Preprint typeset in JINST style- HYPER VERSION Development of wavelength shifter coated

, 904

"... reflectors for the ArDM argon dark matter detector ..."

### Collaboration in Networks: Architectures, Bottlenecks and Throughput

, 2013

"... Motivated by the trend towards more collaboration in work flows, we study stochastic processing networks where some activities require the simultaneous collaboration of multiple human resources. Collaboration introduces resource synchronization requirements that are not captured in the standard proc ..."

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Motivated by the trend towards more collaboration in work flows, we study stochastic processing networks where some activities require the simultaneous collaboration of multiple human resources. Collaboration introduces resource synchronization requirements that are not captured in the standard procedure (formalized through a static planning problem) to identify bottlenecks and theoretical capacity. We introduce the notions of collaboration architecture and unavoidable idleness. In general, collaboration architectures may feature unavoidable idleness so that the theoretical capacity exceeds the maximal achievable throughput or actual capacity. This fundamental tradeoff between collaboration and throughput does not disappear in multi-server networks and has important ramifications to service-system staffing. We identify a special class of collaboration architectures that have no unavoidable idleness and present a condition on this architecture that guarantees, regardless of the processing times of the various activities, that the standard bottleneck procedure in fact identifies the actual capacity of the network. In multi-server cases this class of networks guarantees that the theoretical capacity is achievable provided one has the right number of floaters. Finally, we study the subtleties that collaboration introduces to questions of flexibility investment. Unavoidable idleness may limit the ability to materialize the benefits of flexibility. We study the interplay of flexibility and unavoidable idleness and offer remedies derived from collaboration architecture.

### Polling systems in heavy traffic: Exhaustiveness of service policies ∗

, 1997

"... We study the expected delay in cyclic polling models with general ‘branching-type’ service disciplines. For this class of models, which contains models with exhaustive and gated service as special cases, we obtain closed-form expressions for the expected delay under standard heavy-traffic scalings. ..."

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We study the expected delay in cyclic polling models with general ‘branching-type’ service disciplines. For this class of models, which contains models with exhaustive and gated service as special cases, we obtain closed-form expressions for the expected delay under standard heavy-traffic scalings. We identify a single parameter associated with the service discipline at each queue, which we call the ‘exhaustiveness’. We show that the scaled expected delay figures depend on the service policies at the queues only through the exhaustiveness of each of the service disciplines. This implies that the influence of different service disciplines, but with the same exhaustiveness, on the expected delays at the queues becomes the same when the system reaches saturation. This observation leads to a new classification of the service disciplines. In addition, we show monotonicity of the scaled expected delays with respect to the exhaustiveness of the service disciplines. This induces a complete ordering in terms of efficiency of the service disciplines. The results also lead to new rules for optimization of the system performance with respect to the service disciplines at the queues. Further, the exact asymptotic results suggest simple expected waiting-time approximations for polling models in heavy traffic. Numerical experiments show that the accuracy of the approximations is excellent for practical heavy-traffic scenarios.

### Printed in U.S.A. POLLING SYSTEMS IN HEAVY TRAFFIC: A BESSEL PROCESS LIMIT

"... This paper studies the classical polling model under the exhaustive-service assumption; such models continue to be very useful in performance studies of computer/communication systems. The analysis here extends earlier work of the authors to the general case of nonzero switchover times. It shows tha ..."

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This paper studies the classical polling model under the exhaustive-service assumption; such models continue to be very useful in performance studies of computer/communication systems. The analysis here extends earlier work of the authors to the general case of nonzero switchover times. It shows that, under the standard heavy-traffic scaling, the total unfinished work in the system tends to a Bessel-type diffusion in the heavy-traffic limit. It verifies in addition that, with this change in the limiting unfinished-work process, the averaging principle established earlier by the authors carries over to the general model.

### unknown title

"... Towards a unifying theory on branching-type polling systems in heavy traffic R.D. van der Mei ..."

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Towards a unifying theory on branching-type polling systems in heavy traffic R.D. van der Mei

### Optimal Scheduling of Queueing Networks with Switching Times Using Genetic Algorithms

"... Abstract:- in this paper we consider the problem of optimal scheduling of queueing networks with switching times based on genetic algorithms approach. We propose a special chromosome encoding scheme, crossover and mutation operators. Deterministic mutation is used to prevent premature convergence to ..."

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Abstract:- in this paper we consider the problem of optimal scheduling of queueing networks with switching times based on genetic algorithms approach. We propose a special chromosome encoding scheme, crossover and mutation operators. Deterministic mutation is used to prevent premature convergence to a poor solution. Finally, results of computational experiments are included to compare deterministic mutation with classical probabilistic one. Key-Words:- queueing networks; optimal scheduling; switching times; genetic algorithms; deterministic mutation. 1

### Heavy traffic analysis of polling models by Mean Value Analysis

, 2006

"... In this paper we present a new approach to derive heavy-traffic asymptotics for polling models. We consider the classical cyclic polling model with exhaustive or gated service at each queue, and with general service-time and switch-over time distributions, and study its behavior when the load tends ..."

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In this paper we present a new approach to derive heavy-traffic asymptotics for polling models. We consider the classical cyclic polling model with exhaustive or gated service at each queue, and with general service-time and switch-over time distributions, and study its behavior when the load tends to one. For this model, we explore the recently proposed mean value analysis (MVA), which takes a new view on the dynamics of the system, and use this view to provide an alternative way to derive closed-from expressions for the expected asymptotic delay; the expressions were derived earlier in [31], but in a different way. Moreover, the MVA-based approach enables us to derive closed-form expressions for the heavy-traffic limits of the covariances between the successive visit periods, which are key performance metrics in many application areas. These results, which have not been obtained before, reveal a number of insensitivity properties of the covariances with respect to the system parameters under heavy-traffic assumptions, and moreover, lead to simple approximations for the covariances between the successive visit times for stable systems. Numerical examples demonstrate that the approximations are accurate when the load is close enough to one.