The key challenge in admission control in wireless networks is to strike an optimal trade-off between the blocking probability for new requests while minimizing the dropping probability of ongoing requests. We consider two approaches for solving the admission control problem: i) the typically adopted threshold policy and ii) our proposed policy relying on reinforcement learning with neural networks. Extensive simulation experiments are conducted to analyze the performance of both policies. The results show that the reinforcement learning policy outperforms the threshold-based policies in the scenario with heterogeneous time-varying arrival rates and multiple user equipment types, proving its applicability in realistic wireless network scenarios.

We consider a system with several job types and two parallel server pools. Within the pools the servers are homogeneous, but across pools possibly not in the sense that the service speed of a job may depend on its type as well as the server pool. Immediately upon arrival, jobs are assigned to a server pool, possibly based on (partial) knowledge of their type. In case such knowledge is not available upon arrival, it can however be obtained while the job is in service; as the service progresses, the likelihood that the service speed of this job type is low increases, creating an incentive to execute the job on different, possibly faster, server(s). Two policies are considered: reroute the job to the other server pool, or replicate it there.We determine the effective load per server under both the rerouting and replication policy for completely unknown as well as partly known job types. We also examine the impact of these policies on the stability bound, which is defined as the maximum arrival rate of jobs for which the effective load per server is smaller than one. We demonstrate that the uncertainty in job types may significantly reduce the stability bound, and that for (highly) unbalanced service speeds full replication achieves the largest stability bound. Finally, we discuss how the use of threshold-based policies can help improve the expected latency for completely or partly unknown job types.

We investigate the stability condition for redundancy-d systems where each of the servers follows a processor-sharing (PS) discipline. We allow for generally distributed job sizes, with possible dependence among the d replica sizes being governed by an arbitrary joint distribution. We establish that for homogeneous servers the stability condition for the associated fluid-limit model is characterized by the expectation of the minimum of d replica sizes being less than the mean interarrival time per server. In the special case of identical replicas, the stability condition is insensitive to the job size distribution given its mean, and the stability threshold is inversely proportional to the number of replicas. In the special case of i.i.d. replicas, the stability threshold decreases (increases) in the number of replicas for job size distributions that are NBU (NWU). We also discuss the extension to heterogeneous servers. For heavy-tailed job sizes we characterize the tail behavior of the response time distribution. In particular, for regularly varying job sizes with tail index −ν it is shown that the tail index of the response time equals −ν and −dν for identical and i.i.d. replicas, respectively.