We present a queueing model for a quantum communication network consisting of a primary queue and a service queue in which Bell pairs are formed and stored. The Bell pairs are inherently extremely short-lived rendering the service queue (the quantum queue) much faster than the primary queue. We study the asymptotic behaviour of this multi-scale queueing system via a stochastic averaging principle. We prove a Functional Law of Large Numbers (FLLN) and a Functional Central Limit Theorem (FCLT) for the standard queue averaging the dynamics of the fast service queue.
We present a queueing model for a quantum communication network consisting of a primary queue and a service queue in which Bell pairs are formed and stored. The Bell pairs are inherently extremely short-lived rendering the service queue (the quantum queue) much faster than the primary queue. We study the asymptotic behaviour of this multi-scale queueing system via a stochastic averaging principle. We prove a Functional Law of Large Numbers (FLLN) and a Functional Central Limit Theorem (FCLT) for the standard queue averaging the dynamics of the fast service queue.
The convergence of quantum computing and classical service system modeling presents a transformative opportunity. This paper proposes the formalization of Quantum Queueing Theory (QQT), a novel framework for modeling, analyzing, and optimizing service systems where quantum processors act as servers, quantum algorithms constitute service tasks, and quantum communication channels facilitate arrivals and departures. We outline the fundamental challenges posed by quantum mechanics (superposition, entanglement, measurement, decoherence) to classical queueing paradigms. Key research directions include defining quantum analogues of arrival processes, service disciplines, and performance metrics (quantum fidelity, task success probability, decoherence-limited waiting time). We explore modeling approaches leveraging quantum stochastic processes, quantum walks, and modified Lindblad master equations. The paper details critical areas for future research: hybrid quantum-classical queueing networks, resource allocation under decoherence, stability analysis in the quantum regime, and the development of quantum-aware scheduling policies. QQT is poised to become essential for designing efficient and scalable quantum computing data centers, quantum cloud services, and integrated quantum-classical computing infrastructures.
We study the quality of service in quantum channels. We regard the quantum channel as a queueing system, and present queueing analysis of both the classical information transmission and quantum information transmission in the quantum channel. For the former, we link the analysis to the classical queueing model, for the latter, we propose a new queueing model and investigate the limit queueing behavior. For both scenarios, we obtain tail distributions of the performance measures, i.e., backlog, delay, and throughput.
As quantum networks move toward multi-user architectures, a central question is how the performance of entanglement distribution scales with the numbers of network nodes N and active users M, yet existing studies use different objectives, resource assumptions, and normalizations. To account for delivery distance under multi-user demand, we define entanglement transport, which weights each delivered Bell pair meeting a fixed fidelity threshold by its endpoint separation. In a two-layer framework, (i) a resource layer measures capacity per activation slot under different aggregation regimes, and (ii) a physical layer measures service per second under implementation constraints. For matched implementations with a bounded number of activation slots per second, asymptotic-aggregation capacity sets a service ceiling, whereas achievable service must be established separately. On expanding honeycomb lattices with one random session, fixed-window entanglement-percolation constructions achieve Θ(N−1) entanglement transport per activation slot below their thresholds and Θ(N) above them. For homogeneous chains, asymptotic aggregation exceeds fixed-window capacity by a factor Θ(N2/M), and in spatial expansion a noisy physical implementation achieves Θ(M/N) service per second. These examples show that entanglement-transport scaling depends not only on connectivity but also on resource aggregation and physical implementation. The framework provides a common basis on which quantum-network scaling laws can be established.
We study the quality of service in quantum channels. We regard the quantum channel as a queueing system, and present queueing analysis of both the classical information transmission and quantum information transmission in the quantum channel. For the former, we link the analysis to the classical queueing model, for the latter, we propose a new queueing model and investigate the limit queueing behavior. For both scenarios, we obtain tail distributions of the performance measures, i.e., backlog, delay, and throughput.
We study the quality of service in quantum channels. We regard the quantum channel as a queueing system, and present queueing analysis of both the classical information transmission and quantum information transmission in the quantum channel. For the former, we link the analysis to the classical queueing model, and for the latter, we propose a new queueing model and investigate the limit queueing behavior. For both scenarios, we obtain tail distributions of the performance measures, that is, backlog, delay, and throughput.
In this work we consider a quantum network consisting of multiple interconnected quantum repeaters. In this network, data plane of communication is achieved by photon transmission over fibre cables, while the control plane which transmits results of measurements and control information is implemented over classical Internet. Important part of the control plane is the server which distributes connection requests and entanglement resources to nodes involved in the path. Together, data and control plane establish reliable multi hop links over the network deploying purification and swapping operations. We analyze the performance of such a network using probabilistic model of communication time between repeaters, rather than slotted time. We consider random arrivals of connection requests to each repeater and variable path lengths. We model a single repeater using theory ofM[x]/G/m+rqueues where each batch request encompasses heralding, purification, and swapping times pertaining to a single repeater node. To model the network, we have used the concept of Jackson's network over repeater nodes in the path. This model allows derivation of end-to-end entanglement delivery time as random distribution and calculation of probability of decoherence of qubits stored in quantum memories over the path. We considered different numbers of entanglements per request and different types of quantum memories. Results of this analysis are useful for dimensioning capacities of quantum repeaters, memories and links in order to avoid decoherence of quantum memories.