Structural properties of the optimal resource allocation policy for single-queue systems

Abstract. Heterogeneous servers which can differ in service speed and reliability are becoming more popular in the modelling of modern communication systems. For a two-server queueing system with one nonreliable server and constant retrial discipline we formulate an optimal allocation problem for minimizing a long-run average cost per unit of time. Using a Markov decision process formulation we prove a number of monotone properties for the increments of the dynamic-programming value function. Such properties imply the optimality of a two-level threshold control policy. This policy prescribes the usage of a less productive server if the number of customers in the queue becomes higher than a predefined level which depends on the state of a non-reliable more powerful server. We provide also a heuristic solution for the optimal threshold levels in explicit form as a function of system parameters.

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“…The application of MDP with constraints to the problem of optimal allocation in queueing systems was illustrated e.g. in [35].…”

Section: Optimization Problem For Performance Characteristicsmentioning

confidence: 99%

Optimal Control of a Two-Server Heterogeneous Queueing System with Breakdowns and Constant Retrials

Efrosinin¹,

Sztrik²

2016

Communications in Computer and Information Science

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“…Casualties are already assigned into queues during the triage process. Yang et al (2013) study the structural properties of the optimal resource allocation policy for single-queue systems. Yang et al (2011) generalizes the problem to multiple service facilities and shared pool of servers.…”

Section: Literature Reviewmentioning

confidence: 99%

Staff assignment policies for a mass casualty event queuing network

2017

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“…The optimal policy of their Markov decision process (MDP) formulation depends on the queue length, the number of packet arrivals in the previous time slot, and the channel fading state that governs the power loss in transmission. In [31], authors studies structural properties of the optimal resource allocation policy for a singlequeue system in which a central decision-maker assigns servers to each job. A major challenge in our problem, as opposed to the above works, arises due to SMDP formulation for non-memoryless service time distribution and its unimodal dependence on the cognitive state.…”

Section: Introductionmentioning

confidence: 99%

Structural Properties of Optimal Fidelity Selection Policies for Human-in-the-loop Queues

Gupta¹,

Srivastava²

2022

Preprint

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We study optimal fidelity selection for a human operator servicing a queue of homogeneous tasks. The agent can service a task with a normal or high fidelity level, where fidelity refers to the degree of exactness and precision while servicing the task. Therefore, high fidelity servicing results in higher-quality service but leads to larger service times and increased operator tiredness. We treat the cognitive state of the human operator as a lumped parameter that captures psychological factors such as workload and fatigue. The service time distribution of the human operator depends on her cognitive dynamics and the fidelity level selected for servicing the task. Her cognitive dynamics evolve as a Markov chain in which the cognitive state increases with high probability whenever she is busy and decreases while resting. The tasks arrive according to a Poisson process and each task waiting in the queue loses its value at a fixed rate. We address the trade-off between high-quality service of the task and consequent loss in value of subsequent tasks using a Semi-Markov Decision Process (SMDP) framework. We numerically determine an optimal policy and the corresponding optimal value function. Finally, we establish structural properties of an optimal fidelity policy and provide conditions under which the optimal policy is a threshold-based policy.

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Structural properties of the optimal resource allocation policy for single-queue systems

Cited by 13 publications

References 22 publications

Optimal Control of a Two-Server Heterogeneous Queueing System with Breakdowns and Constant Retrials

Optimal Control of a Two-Server Heterogeneous Queueing System with Breakdowns and Constant Retrials

Staff assignment policies for a mass casualty event queuing network

Structural Properties of Optimal Fidelity Selection Policies for Human-in-the-loop Queues

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