{"uid":"cap_BUUHFhQep7kGFush0gMVE","slug":"compute-siliq-io-73b90732","name":"Erlang C / M/M/c Queuing Theory Calculator","description":"","url":"https://compute.siliq.io/analytics/erlang","method":"POST","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method","bodyType","body"],"properties":{"body":{"properties":{}},"type":{"type":"string","const":"http"},"method":{"enum":["POST","PUT","PATCH"],"type":"string"},"bodyType":{"enum":["json","form-data","text"],"type":"string"}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object"}}}}},"responseSchema":null,"example":{"request":{"input":{"body":{"num_servers":12,"arrival_rate":150,"service_rate":15},"type":"http","method":"POST","bodyType":"json"}},"response":{"prob_wait":0.4494,"utilization":0.8333,"service_level":0.9998,"system_stable":true,"interpretation":"Moderate load — 83% utilization. Consider adding servers before peak demand.","compute_time_ms":0,"avg_queue_length":2.247,"avg_wait_time_hours":0.015,"recommended_servers":11,"avg_system_time_hours":0.0816,"recommended_servers_utilization":0.9091}},"exampleRequest":{"num_servers":12,"arrival_rate":150,"service_rate":15},"tags":["x402"],"displayCostAmount":"0.01","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"settled","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"down","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.01/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.01","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.01","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_mF5z1gMGhtoacapjsEQhG","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.01","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes Erlang C wait probability, service level, and staffing recommendations for M/M/c queuing models given arrival rate, service rate, and number of agents.","exampleAgentPrompt":"We get about 150 calls per hour, each taking an average of 4 minutes to handle — can you run an Erlang C calculation to tell me how many agents we need to hit an 80% service level within 20 seconds, and what the wait probability would be at that staffing level?","exampleUseCases":null,"resultDescription":"Returns Erlang C wait probability (probability a caller must wait), achieved service level percentage, recommended number of agents to meet a target service level, queue utilization, and estimated average wait time for the given M/M/c parameters.","failureModes":["Invalid or negative arrival/service rate returns 400 validation error","Agent count of zero or utilization >= 1.0 (overloaded system) returns error indicating infinite queue","Missing required parameters returns 422 unprocessable entity","Payment failure or insufficient USDC balance returns 402 payment required","Extremely high traffic intensity may return numerical instability warning"],"whenToPreferThis":"Choose this endpoint when you need rigorous Erlang C / M/M/c queuing theory calculations for contact center staffing, support queue sizing, or any multi-server queue analysis. Prefer over general statistics or simulation APIs when you specifically need closed-form Erlang C metrics including wait probability and service level. Ideal for workforce management automation, real-time staffing adjustments, or SLA planning.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T17:26:40.938Z","isFirstParty":false}